2 turntables and one phono stage - Can I???

Thanks for all of the replies. Doesn't appear to be a safe and secure way to deal with this. I guess those who have multiple armed tables have to deal with this issue as well.
Seems like the best way to deal with this is to keep the two set of RCAs close and continue to manually swap them. I like the idea of getting a second phono stage, thanks.
BTW, although it doesn't matter much, the two tables are in a different system than the one pictured in my virtual systems.
The two tables I am swapping out are a Basis 2500/Vector/Benz Ruby H and Clearaudio ReferenceTG1/Clearaudio Signature M cartridge the Phono Stage is a Thor TA3000.

Thanks All

Almarg, I was in a way responding to the (good) point that you made. To do this properly, you need to isolate the lead carrying the "ground" side of the cartridge output (which as you correctly state is merely the other side of the coil from hot) from both chassis ground and the shield around the phono cable. Chassis and shield leads can be connected to the chassis of the switch box and hence back to the preamp. Then switch BOTH sides of the coils of both cartridges, with no ground reference, using a DPDT. It occurs to me that you would need two DPDT switches, one for each channel, or one 4PDT switch.

there is luxman,gold PH-10 , Musical Fidelity LX-LPS  that has two inputs for 2 turntable at same time that can be selected phono1 or phono2.