Inclusive proton spectra for the reactions #d~3rcp, #d ~ 5rcp, and #d ~ KKmrcp are calculated. In addition to nucleon exchange, the rescattering of pions and kaons, and the production and absorption of heavy mesons is evaluated. In the proton spectator momentum regime of 200 to 600 MeV/c, the role of heavy mesons is found to be negligible. The proper counting of the topological variants of pion and kaon rescattering can explain the cross sections with the exception of the #d ~ 3rcp channel.