I like the version where instead of altering the future when you go to the past and alter things, you snap off an entirely new independent timeline. AKA Nothing you do will affect the timeline you came from when you hit the "Return to Point of Origin" button. AKA Dragonball Z time travel.

You can totally go one day backwards and kill the past day version of your own self and you will continue living because you clearly did not die in your timeline, yet. Then you could go another day further back and grab you from the past and bring yourself to the future. Multiple you would be fine because, although you were never recruited by yourself, you gained the ability to recruit yourself later.

Splitting timelines might make some of them collapse, dunno if it's possible in the first place, but I like this version for storytelling.

You can have your cake AND eat it. But you can never change mistakes from your own time, you have to live in an always-moving-forward way.