Need to get your breakpoint away from theirs.
If it's on a house pattern I usually resort to the boomerang pearl ball and use a breakpoint outside of theirs and hope I don't miss in to their traffic, because the ball will wiggle on the carrydown and you never know what will happen.
Other option is to grab something stronger and get inside of them, and hope you don't miss outside and hit their traffic, because again your ball will wiggle.
Usually it takes more than one person tossing urethane to affect the pattern a lot in my experiences, but every environment is different and if you play the same spot on the lane, guess it could be more substantial