Change the perspective.
Honestly, you could do this for a series in the Prime Universe, but change the perspective of how we're introduced to the Federation and the concept of Starfleet.
Have the main character be from a race that's newly inducted to Federation membership, show that society adjusting to what it means to be in the Federation and be under Starfleet protection (e.g., showing both positive and negative aspects, debates between factions, etc.), and then follow his journey to becoming a Starfleet officer.
You can use his journey to question and deconstruct everything about the nature of Star Trek.
Honestly, you could do this for a series in the Prime Universe, but change the perspective of how we're introduced to the Federation and the concept of Starfleet.
Have the main character be from a race that's newly inducted to Federation membership, show that society adjusting to what it means to be in the Federation and be under Starfleet protection (e.g., showing both positive and negative aspects, debates between factions, etc.), and then follow his journey to becoming a Starfleet officer.
You can use his journey to question and deconstruct everything about the nature of Star Trek.