Will the cage under the top tube take a full size bottle, piggyback shocks notwithstanding, and does it fall out at every given opportunity?

I haven’t been able to find a bottle/cage combination that will fit in there at all on my medium frame. I tried one of those Fabric cageless efforts, because they were supposed to fit, but it fouled on the shock (Cane Creek DBInline Air) and scuffed up quite badly over just one ride. There might be some other alternative I’m not aware of, I gave up trying after that as I usually ride with a pack anyway.