It can be done, but you have to be careful as the copper connections on the refrigerant lines can be loosened by movement. Years ago, in my first house my heat pump was under my deck for the first floor. I had a walk out basement. I was pouring a patio under the deck and needed to get the compressor out of the way. I rigged up a hoist and lifted it up about 6" to allow me to pour the patio under the unit. I was successful, no damage.
For yours I'd probably use a digging iron to lift the low side and then insert bricks under the pad to level it. Once it is level you could fill the space with polyurethane foam leaving the bricks in place. Given the cost of refrigerant these days pulling the unit and setting a firm foundation and replacing the unit would cost a lot of money. The refrigerant would need to be removed and recycled and new refrigerant installed. I'm not a HVAC tech, but I don't think it can be pulled out and put back in, I could be wrong though.