A number of gyms recently have been creating Conjugate/CrossFit hybrids, where some Westside style work is followed by CrossFit style conditioning, sometimes using conditioning work for some of the accessory work (might have exercises like weighted lunges or glute ham raises as part of a high intensity circuits on a lower body day, for example).
I think the mix of speed work, max effort work, and high rep assistance work, along with constant variety, makes conjugate methodology a great fit with CrossFit, as CrossFit also values a broad range of abilities and frequent variety.
Some examples of gyms I've found using versions of this:
Have you tried a routine like this? Are you trying one now? Are you curious? Right now I'm mixing the two workout methods on lower body days, and doing pure Westside style upper body days (Coach Rick Scarpulla is helping me via the phone and internet on my upper body stuff. My bench sucks and I don't want it to anymore).