For me I would say “The Expanse” is a huge one. If there was ever a self made family, the crew of the Rocinante is one of the best. The amount of time they spend together and how they congeal into life long partners and friends in the face of some truly awful events is really inspiring to me.
I love and hate the Expanse because it’s entirely believable that we’d finally clear out the bullshit infighting/politics on earth today just to trade for bullshit infighting/politics in space. It’s realistic if a bit depressing in such. :-) The actual acting is also pretty great in the show, and the relationship between the crew kinda reminds me of Firefly.
As far as sci-fi shows go, The Orville was also cool this way, if a bit goofy at times. The crew acts like a large family in many ways but with a diversity of cultures/personalities that are used to reflect real societal issues kinda like the old Star Trek series did.
In terms of books… the Spellmonger series has a bunch of characters that aren’t all related but have a fairly familial relationship with each other.