Depends on how the air return is attached. That space you show in the picture looks quite tight. If you need more space it would be better to buy a larger house than trying to rob space from the HVAC system.

Are you nuts: land is expensive.

HVAC redesign isn't exactly cheap, not redesigned properly and then you wonder why it doesn't heat or cool properly. (summer is coming, get your tickets now)

I service the Katy, Texas area.

And I'd take those plastic bags off the furnace before the heating season comes around!

The air handler can be raised, but unless you relocate the plumbing on the left the height will be limited. It seems you will spend quite a bit of money to gain a small storage space.