The development of microscale devices that autonomously perform multistep processes is vital to advancing the use of microfluidics in industrial applications. Such advances can potentially be achieved through the use of "chemical pumps" that transduce the energy from inherent catalytic reactions into fluid flow within microchambers, without the need for extraneous external equipment. Using computational modeling, we focus on arrangements of multiple chemical pumps that are formed by anchoring patches of different enzymes onto the floor of a fluid-filled chamber. With the addition of the appropriate reactants, only one of the enzymatic patches is activated and thereby generates fluid flow centered about that patch. These flows drive the self-assembly of microparticles in the solution and localize the particles onto the activated patches. By varying the spatial arrangement of the enzymatic patches, and the sequence in which the appropriate reactants are added to the solution, we realize spatiotemporal control over the fluid flow and the sequential transport of microparticles from one patch to another. The order in which the particles visit the different patches can be altered by varying the sequence in which the reactants are added to the solution. By harnessing catalytic cascade reactions, where the product of one reaction is the reactant for the next, we achieve directed transport between the patches with the addition of just one reactant, which initiates the catalytic cascade. Through these studies, we show how the trajectory of the particles' motion among different "stations" can be readily regulated through intrinsic catalytic reactions and thus, provide guidelines for creating fluidic devices that perform multistep reactions in an autonomous, self-sustained manner.