Do people who are registered in multiple places, vote in multiple places? Of course. Is it a problem? Of course, but I don't think it's enough to swing elections.
Where the problem lies is with the *OLD* unused, outdated registrations, the ones nobody cares about. Dead voters, people who've moved away, and so on. Cleanup for something like this is simple, but many districts refuse to do it, for reasons that are obvious. Unscrupulous poll workers can vote them, any way they'd like, in some places by the bushel basket full.
How else do you think some places get 105% voter turnout, or 117-year-old people casting ballots?
That has been reported, but to date I've not seen any documentation that proves the crime. Why is it not being fully investigated, now that the adults are in charge?