<p>We study consistent (allocation) rules in multi-unit object allocation problems with money. Objects are identical and preferences of agents are multi-demand but may not be quasi-linear. We consider the class of weakly object monotonic preferences and that of single-peaked preferences. We first show that on those domains, if a rule satisfies consistency, strategy-proofness, individual rationality, no subsidy, independence of unallocated objects, non-wasteful tie-breaking, and minimal tradability, then it is a sequential dictatorship rule. Since not all sequential dictatorship rules satisfy strategy-proofness, consistency, and independence of unallocated objects, we then focus on a specific class of sequential dictatorship rules called sequential dictatorship rules with the smallest number tie-breaking. When preferences are weakly object monotonic and the reservation prices are non-decreasing in the number of objects, sequential dictatorship rules with the smallest number tie-breaking satisfy consistency and independence of unallocated objects if and only if there is a common priority ordering for two or more objects and it is an acyclic ordering of the priority ordering for one object. We also show that this characterization holds without the assumption on the reservation prices when preferences are single-peaked.</p>