Sure. You can install blocks to support the boards that give too much...and you can install thin wood strips to the back of the boards to seal the open gaps. Simple.

Thanks. What about whole strips of plywood between the joists? How would you put this up? Basically, much of the floor is getting damaged by walking on it since original hardwood floor.

You could cut strips of plywood, insert from underneath and support it with some short lengths of 1x2s screwed horizontally into the joists using a screw gun. You could even apply something like Liquid Nails to the top of the plywood before pushing it up against the bottom of the old floor.

Thanks, that sounds like a great idea!

"You could cut strips of plywood, insert from underneath and support it with some short lengths of 1x2s screwed horizontally into the joists using a screw gun. "

Cut plywood to fit between joists, sister pieces of 2x2 to the sides of the joists to hold it in place.

liquid nails is a BAD idea.

Agree with that one!