Double would be a COP of over 10. That's a stretch for an overbuilt GSHP and not even slightly feasible for air-air.
High COPs are usually easy on a compressor as they represent low compression ratios and low differential temps. For example I can hit around COP 7 in cooling on my scrap heap GSHP, with an evap temp around 10C and condenser temp around 20C. That's a high side pressure around 100 psi and only 30 psi of differential, "barely working" as far as the compressor is concerned.
The only way I know to get high COPs is to have an oversized condenser and a way to get your refrigerant below ambient, like evaporative, ground source or overnight radiant so you can get the compression ratio down, unless you know a secret in which case I'm not afraid to burn out a compressor or two trying it out!