Now that I beat the game, I notice you can interect with Shaun and continue with the faction you choose which gives you more quests but I was wondering if I continue is there a second ending because it seems like there is something unfinished?

I think like Skyrim there can be a lot more to do, but the MQ is over.

I was kind of hoping maybe the minute men would have some kind of secret quest after you've acquired every single settlement in the wasteland under them but it doesnt seem to be the case.

No 2nd ending if you continue to play. There are still side quests and faction quests

Well, assuming the faction in question is still around. The faction you 'picked' at the end will generally have endless random quests for you. But you know how fun those get after a while.

More fun???

Just thought it was strange because the one faction I picked, their quest at the end have a number that keeps increasing which made me wonder if that was one of those "infinite" missions that keep coming back. Plus the whole Shaun thing felt incomplete like there should have been at least some finality option giving like making a special house for him.

Theres 4 endings, one for each faction. You obviously need to start again to experience the others..

If anything, dont play them for the endings - theyre all vaugley similar - infact, now i withhold from the story because once its done.. Youre kinda sat there like "well.. Now ive done everything. Great. Grand. Fabulous. What now? Side quests? Oh. Yey."

Well in my BoS ending both older and younger Shaun didn't make it, so ... no real issues there. I honestly loved how the BoS ending set you up to continue your missions and self-questing. After I've tried all the endings and want to pick one for my 'real' play-through I imagine that's the one I'm going with. MM are too much maintenance with all the settlement issues just 'popping' up all the time. RR are just nuts. Institute is just ... well not real conducive to continued play on the surface.

If you ended the MQ with Minutemen or BoS, you can start the "Destroy BoS" questline with Minutemen if you want to.

Other than that, maybe some DLC gives a second ending. But as far as the Sole Survivor's story for finding and dealing with his son goes, that story line has ended.

Mods and DLCs my friend, mods and DLCs.

Didn't New Vegas also have two endings? I can't remember....

It had four I believe (NCR, Legion, Mr House, Yes Man)

But didn't each one of those had credits at the end?

Yeah, that changes depending on which side quests and faction quests you did during the game. Something I really miss

I am wondering if they leave it open at the end like that for the expansion packs so people can level and get prepared.