Andy replies:

If I were you, I would hire a registered engineer to evaluate
your problem. You may NOT be able to do this without
injuring your neighbor's property, either thru excavation and
possible cave-in, or water drainage damage. And be assured
that if you do something to YOUR OWN property that damages
YOUR NEIGHBOR'S property, you will have bigger problems
to solve.....

Also, a registerd engineer can tell you where all this
extra water is supposed to go to. It may not be allowed
to drain the local water table into the local sewer system,
or into the street, or into the neighbor's yard....

Get over the idea that you can do anything you want
to your property. There are both civil and criminal laws
which prevent your actions if they cause damage to
anyone else....

Andy in Eureka, Texa