The opener of S2 would have Voyager making it out of the Periphery, past Cullah's group of Kazon Pirates and enter the central core where the major powers and central worlds/commerce areas and stuff are, hoping they can find some ports to stop and do repairs and maybe find more information on where they are. There is in fact a large Station that serves as an entry-point into the Central Core from the Periphery. It’s a military base to repel invaders as a port of call for any non-hostiles who want entry. Think of it as the equivalent of a Babylon station. It identifies itself as a League Guardian Outpost.
The dominant power in the Core is The League of Space faring Civilizations, a multi-species group that was originally formed as a military alliance for mutual defense against their greatest foe (known only as the "Fluidics") that eventually evolved into a Federation-esque group, only with more of a military bent. They put less emphasis (little to none) on purely scientific or exploratory endeavors and dedicated their sciences and star forces to military applications. The only explorations or archeological missions they undertake are to uncover and seek out alien technologies for their own advantages.
They became so military-oriented that they eventually started ignoring the lesser wars and plights of non-League civilizations (not doing anything to help the Vidiians fight the Phage, or end the Haakonian Occupation of Talax) so they could focus more on their own defenses (because they're so scared of the Fluidics who are IMMENSELY powerful). They're not bad guys or some generic space military state, but they have military bases and garrisons on practically every League world and colony; however the civilians all understand their need and are grateful for their presence.
Imagine the meeting from the beginning of Trek VI, only they're discussing increasing militarization and mothballing their scientific and exploration branches to increase military spending (they use a capitalist economic system).
So as long as VOY obeys their laws and stuff, they can use their ports and trade, and the League may even rescue them from Kazon Pirates if it's in their patrol space, but once VOY leaves League influence (or even the outer reaches of League space, at the very beginning of entrance into the nebulas/asteroid fields/empty systems leading to the Periphery), they're on their own against pirates and stuff because the League isn't interested in defeating the Kazon pirates once and for all and saving anyone in the periphery.
League Of Spacefaring Civilizations
Size wise, they're a little smaller than the Federation, and maybe technologically on par in some areas, below in some others (because of the military bent) and superior to them in ship design and military technologies.
The League's best ship would be similar to the Voth City-Ship, which is a "Mobile Command" they only have a handful of. They serve as mobile HQs and Super-Flagships. To borrow from Star Wars they have automated battle drones that serve as their smallest craft (sorta their take on Fighters). Like the Battle Drones from TNG's "Arsenal of Freedom".
As for the League's weapons, they're basically supposed to be what if the Federation was near-totally militant with little to no scientific or exploration divisions. This would mean they're more rigid in tech development and don't have the "Jack of all Trades" style that the Federation uses. But they don't grow expendable clone armies to be sent out to die or make mass-production warships that are meant for ramming and stuff like the Dominion does either. They try to make mass-production ships that can hold up in a fight, and their military is made up of trained League citizens who volunteer for service (like a regular military).
So their ship-building skills are below the Dominion's because they try for quality AND quantity, and they're more rigid in design than the Federation. But they do have superior vessel design with more powerful weapons, hulls that are harder to breach, good military training and tactics, more maneuverable (isn't very good as a warship if it's a lumbering brick.)
To command a Mobile Command, you have to be at least a Senior full Admiral, or a Fleet Admiral. That’s how important/powerful it is.
In general, their ships are larger than Federation or Dominion ships, with the Sovereign maybe being their equivalent of a Heavy-Destroyer, but not a Cruiser.
The other powers would be the Krenim, who're going through a new expansionist campaign due to a military uprising on the Krenim homeworld against the Ruling Imperial family.
The Devore Imperium, who're very anti-telepathic, due to the "Great War" 2000 years ago which involved telepathics enemies who used their abilities to great offensive effect.
The Heirarchy and the Malon, just to add some more names and stuff in to flesh out the region.
Think Tank here would be a private corporation that sells itself out to solve problems for other races (incurable diseases, super computer viruses, new ship or weapon designs), for extremely high fees of course. Their HQ is a station built around a Micro-Star they created which is their power source.
It'd be revealed that the reason Cullah was so determined to get his hands on Voyager wasn't because he wanted its tech, it was because he's been trying to apply to the League for Kazon membership and kept getting rejected because they don't offer anything worthwhile to the League's well-being. He saw that VOY's tech was around League level and thought of capturing it and presenting it as a gift to the League.
The VOY crew would have to do more work and stuff once in League space to earn money to pay for the ship repairs, do trading and gather information and allies once they're past the Periphery area and don't have to worry about any more Kazon or Vidiian attacks if they stopped anywhere.
Story-wise S2 would open with the crew splitting up inside the Outpost: Some staying to supervise repairs, some going to see what trading can be done/information can be gathered, and some crew going with Neelix to find some friends of his who might be able to help as allies. Here we'd run into some Talaxian ex-soldiers working as mercenaries, with their leader willing to help out as an escort because Neelix is an old friend. But others in the squad would be hostile to the idea because they remember how Neelix also went AWOL and turned his back on the military effort, even though they would've lost anyways.
The information gatherers would discover that whatever maps they can get aren't very helpful because the League hasn't done much deep exploring in a very long time, they've been focusing more on defenses and military tech to defend against the Fluidics that they hadn't gone on any exploration missions for centuries. The best map is an old one that goes out only as far as a 900 light years beyond the Periphery, and it doesn't match very well with any Federation maps they have in the Astrometrics Lab.
They'd have more run ins with maybe some occasional League soldiers who have a grudge against the Talaxian escorts, as well as more benign League soldiers who end up rescuing them or lending a hand when they get in trouble, as well as VOY searching around League space for more information from maybe the black market on anything that can tell them where they are, like DNA testing to see if any others of any of the various Fed species have been around here before, or anything close to them (yeah it's a Farscape rip, but they were in the same situation...). The remaining tension between the Maquis and Fed crews would settle down by now, as they accept that they have to work together and co-exist if they want to survive and Janeway has proven herself a worthy leader.
I've been watching Nausicaa and as such I've decided that the League Commodore/Admiral that VOY would encounter most of the time as the Sector Commander of the League forces they may run into would be a female cyborg with a powerful authoritative presence and her second would be like Kurotawa.
When the VOY crew are trying to learn more about the major races they'd find out that the robotic armies from the "Prototype" episode (of the actual TV show) are the main army of the Lokirrim Union, who are AI-Dependent for a lot of things (they're the ones who hated Photonic beings in canon). This would be the arc after the Outpost one, running into the Lokirrim and their AIs.
To recover from the Fluidic Wars they started using lots of robots after they got their FTL capacities back and started re-establishing their colonies on ravaged worlds or re-establishing contact with surviving colonies (The Fluidic War survivors weren't just left ravaged by the wars, some were blown back to an early industrial state and had to re-develop FTL all over again).
Anyways, several Lokirrim are angry at the mass-usage of AIs since it takes jobs away from real Lokirrim, or they are afraid of what will happen when their AI becomes too powerful. But they rely on them too much to just stop using them without weakening themselves.
Some Lokirrim who are in the army (regular Lokirrim can join, but most don't because they prefer the AIs dying in their place) are somewhat hostile upon meeting VOY due to the Doctor, while others are more accepting because of all the help the AIs have done for them.
There are renegade AIs in the Lokkirrim, modified military Robots who no longer have the programming blocks that keep them loyal to the Lokkirrim. They're mainly terrorists or pirates attacking Lokkirrim shipping or bases (and maybe occasional independent ships, but not major power ones like League vessels) so they'd encounter VOY as well.
As a hint of things to come I'd reveal the main group of Lokirrim robot revolutionaries are under the leadership of the AI from the Think Tank, but it would seem Korris and the others are unaware of what it's doing.
Seska would've been discovered and driven of by this point, having gone to the Kazon and learnt the truth behind Cullah's actions towards Voyager (wanting it as a bargaining chip to get membership in the League), things going as they did in the real show, with some traitors on VOY loyal to Seska and stuff, meeting Denara Pel, etc. The B’Ellanas would discover that they are decomposing, due to the incomplete duplication process used (it was meant to be temporary to begin with) and the Doctor can’t stop it.
Seska starts a re-organizing plan of Cullah's forces to make them into a fighting force capable of taking Voyager. It turns out that most of their bad luck in combat with VOY was primarily due to poor vessel deployment and poor equipment, due to Cullah's incompetence as a tactician and resource manager, making them more a force to be reckoned with.
B’Ellana and Chakotay would leave, since she and the other B’Ellanas have come to a personal conclusion over something and feel it’s the right thing to do. They tell Janeway that they'll be back.
Voyager would come to an area of League space that's near the edge of it, where they could come under attack and wouldn't be able to rely on a League Patrol Cruiser picking up their distress if the Talaxians can't defend them.
The same set-up as the first part of "Basics" would occur, with a Kazon suicide agent getting onboard, the new-and-improved Kazon force attacking and out-manuevering Voayger, the suicide bomber would detonate, further damaging the ship. Realizing that this may be it, Janeway pulls a Captain Forrest and orders everyone to abandon ship while she stays behind to try and distract the Kazon long enough for them to escape with the Talaxian escorts.
Alone on the ship as everyone leaves, Janeway keeps fighting at Tactical with the bridge exploding in sparks and flames all around her (Seska wants to blow up the bridge first to kill off the senior officers before the Kazon take the ship), and the screen would fade to black and as the Exec Producers names appear, a huge explosion is heard. To be continued.