Check out my post below as it is much better!
It would be hard because that would require a 3T or DT on-off-on relay which are hard to find. In fact, on my brief internet search I only found a guy on Ebay selling a used SP3T relay, so I wouldn't call that a viable option.

What is easy though, is to footswitch between 2 different options using a DPDT or SPDT relay. The simplest option is to have one way automatically hard-wired to normal and on the other side letting you choose(on the amp) between Thick and Thicker. The existed switch on the amp would preform that function. It would let you footswtich between normal and thick/thicker.
The hard and complex option is to footswitch between two full options(i.e. thick and thicker) which would be hard because a second switch(on the front) and pair of capacitors would need to be added.
To do the easy one would require adding a jack on the back(or using the reverb jack*) and adding a relay to the amp. The relay supply would be easy but a space on the PCB or a separate PCB for the relay could be tricky.
Zest
*This itself would require rewiring of the reverb jack.