P. 562 of FA2012 says that haemoglobin has positive cooperativity (as we all know), but that it also has "negative allostery." What is the latter referring to?
It's referring to the effect of 2,3-DPG. It binds to an allosteric site of hemoglobin and reduces the affinity of Hb for O2. This promotes a half-unloaded Hb to unload all its O2.