Stubborn crank? Sounds like my neighbor.

Seriously, square taper cranks can take lots of force to remove. But before lean on the wrench, back off the pusher and make sure it pushes directly against the spindle and not on a washer or the crank arm itself. (some removers have larger pusher pads for the larger diameter spindles)

Also make sure the remover body is threaded all the way into the crank arm (usually 5+ turns). Trying to remove a tight crank with the remover not fully engaged is an easy way to strip the arm.

Once you've checked that all is as it should be, go ahead and really lean into the wrench until something gives. (if it's the right crank, make sure you won't slam your knuckles into the chainring when it finally goes)