Yes you can use it like that . I think, the example you gave are correct.
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"I got over (with) it" (maybe a bad habit..)
"We got over (with) it" (maybe an issue..)
Prpleget over withThere are two expressions like this, and you may be confusing one with the other.
PrpleCan I say: "In the beginning there were a lot of problems to get it over with" ?No. I'm afraid not. Problems are not unpleasant procedures that you might want to undergo soon just to be finished with the pain.
PrpleI think I've had a conversation with an English person and he said: "I bet there are a lot of things to get over with".It could be that someone said that, but it sounds strange to me. I'm not sure what that person meant.