We investigate the effect of inter-particle interaction on the quantized Thouless pump in the bosonic quasiperiodic Aubry–André model and find that the quantization of the pumped charge breaks down already for weak interactions. Furthermore, the pumped charge undergoes sharp changes as a function of interaction strength that we can attribute to the closing of specific doublon channels. As expected, the quantization revives in the hard-core limit at very large interaction strengths where the bosons are subject to a hardcore constraint. Interestingly, the stability of isolated doublons under the pump depends on the band they are in. For repulsive interactions and a suitably fixed pump period, doublons in the lowest band are pumped stably while doublons in higher bands dissociate during the pump with one particle decaying into a lower band. This asymmetry leads to the decay of the total energy over time, in stark contrast to the typical Floquet heating expected for a driven many-body system.