Plenty of room down there
"To all available evidence, we have got all the particles down pat"
No! We have the standard model particle zoo caught and stuck on the wall. What we don't have are supersymmetric particles, which are likely going to need something bigger than the LHC eventually (only a few -ino particles are predicted to come into the range even the enhanced LHC can see), and besides that, we want to BREAK the dang standard model if at all possible, because it has to break at least a little to unify to gravity.
The proposed accellerator is likely too small, but as big as political realities allow even for discussion right now. It may also be that it has to be this big - too big a step up and you don't have anything energetic enough to run through it. CERN is a wonderful set of accellerators, some half a century old, that gradually speed up incoming particles for injection into the LHC.