Well, we know from VOY's "Thirty Days" that there is a such thing as the Federation Naval Patrol.
Which sounds like a separate service.
I myself like the idea that the Federation has its own Federation Army and other branches alongside the Federation Starfleet, but the canonical evidence seems to imply that Starfleet's unique force-projection abilities have mostly rendered conventional armies and other forces obsolete.
Yes and no. I could see the Marines becoming the mobile, power-projecting ground force, and the Army becoming a garrison force that drills and defends a specific place - usually major colonies and core worlds. In other words, the army no longer deploys; the Marines do all that. This would permit a much smaller Army - which would be more politically palatable, because many think armies only exist for defense and conquest, but navies have a much broader remit, and marine forces are seen as an adjunct to that. So the UPF could easily maintain a UPFMC/SFMC larger proportionally than today's US ARMY, while having a rump Army just big enough to man defense installations on selected planets, and all the big-idea visioneers who want to believe in a peaceful, non-military Starfleet can convince themselves that SF is really a super-NASA that can fight when needed, and the MC are just a tool they keep for when that becomes necessary, but that they have just enough Army to hold their homes safe - rather like the big-idea men in the late 18th century wanted a militia, not a standing Army, to provide for adequate defense without permitting conquest.
Of course, the Dominion War and various other wars begin to show that a purely garrison force doesn't suffice, and a rapid-response MC force can't bring the heavy firepower a real, mobile, deployable Army can, and so the policy is actually not as wise in practice as it seems in politics and theory, but that veers into wider territory...
And it's not implausible that Starfleet might encompass multiple service branches. The Canadian Forces encompasses the Canadian Army, the Royal Canadian Navy, and the Royal Canadian Air Force, all under a single service force.
But then I'd expect Kirk, Picard, et alia to refer to themselves as sailors or spacers in the Federation Starfleet Navy.