If you have city water and it keeps backin up ...you need to contact your local authority as to what they suggest for your area.
A bathroom in the basement is the lowest plumbing which will be affected now...but if you were to put the overhead new plumbing pipes in you could still have the problem only higher this time.
You need to talk to your local guys because only they know how high the pipes in the street are compared to the home exit lines.
This is a big problem when the rains start.
They sometimes may also be responsible for the problem
....and the solution.