If your MuIII needs rehab (caps, op-amps, etc), Richard is a good choice.
A possible consideration/reason to not get the True-Bypass, and the Gain-Bypass mods, is that, a True-bypass pedal will do the same thing as an internal True-bypass mod, and having the gain knob remain functional when the MuIII effect is bypassed is nice to have also.
For example, if you have the MuIII effect on, you can switch it in/out with the True-bypass pedal.
If you have the MuIII effect off, it is now a additional Gain-stage knob which can be toggled in/out with the true-bypass pedal.
One observation I have made is that the Mu-Octave Divider pedal sounds stronger when it is followed by the MuIII (The octave note actually sounds better/stronger wether the MuIII effect is in or out), presumably becaue it gets the boost of the MuIII's gain stage.
I have 3 MuIII's (best sounding one has never been modded or rehab'd in any way) and two Mu-Octave Dividers (both have been to RL for rehab and have had True Bypass mods, although I usually leave them "on" at all times, and toggle them in/out from the true-bypass pedal) and an 8-loop true bypass pedal. These observations are from my own personal test-fires, and as always, ymmv... no wadgering, please.

Here's that pic of Jer's MuIII with the "In/Out' switch. I know there was a time before True Bypass or "Ground-Control" pedals were common, whereby some guys defeated the Gain function when the MuIII effect was off, in order to not have an un-wanted Gain stage in the line. RL offers that mod as well as TB and general rehab, so you do have choices/options based on your needs.
If JG just wanted to leave the MuIII effect on all the time, and control it from a loop pedal, he wouldn't have needed that in/out switch.
http://dozin.com/jers/90srig/90srack.html