If you're going to envision a multiverse, this might be more of a Worldbuilding SE question. The whole point is that you can't alter your own timeline, and thus screw up causality. But what if you can save a different future you from making the same mistakes?
In my vision of time for worldbuilding, time isn't simply linear, but can be viewed as a three-dimensional object that we can only see one dimension of at a time. So our existence is as a three-time-dimensional being only experiencing one dimension at once. There is a future you one fraction of a second ahead of you in a parallel universe, and a parallel you a fraction of a second behind. So your perception of time would be like an infinite stack of sheets of paper. You can intellectually understand time to be bigger, but you can't see it. The past is truly the past, but in the parallel universe, it's fractionally off in time. So in reality, if you travel across enough parallel universes, every moment of "the past" is happening somewhere RIGHT NOW.
In my story, the MC's future self has been spending their life jumping in time, trying to prevent their past self from experiencing the same pain they did from the loss of their beloved. They keep diverting themselves away from meeting their beloved to spare them the pain. The MC figures out this interference, meets her future self in the past, and agrees to let the future self keep meddling in the past. Besides, it was a different future self that meddled in the MC's past when it happened to HER. But in reality, the 3D time allows all these things to be happening in the current time.
The true MC is actually a three-dimensional-time being, but the nature of human existence is such we can only experience it one dimension/slice at a time. They affect the past because it affects their 3D time self, even if they themselves never get to take advantage of the changes to the past.
- Never mind that people can travel to the past to experience it (and how awesome is that?)
- Never mind tripping to the future to get advanced tech to reshape your world.
- Never mind migrating your culture to the deep past to avoid the supernova destroying your world.
- Never mind winning the lotto, or investing in a major company, then cryo-storing yourself until the stock explodes and you're a billionaire.
- Never mind playing God and convincing people you are a divine being, or conquering the world because you can for fun and profit.
The opportunities of playing with time are endless, even if they can't kill their grandfather for real, and killing Hitler helps someone else. What about your alternate self, alternate world, or alternate home? After all, you don't need to worry about breaking the past if the past is someone else's present.