It is commonplace for modern CPUs to have multiple execution units. The simplest arrangement is to use one, the bus manager, to manage the memory interface, and another to perform calculations.
Some CPUs have as many as five independently executing execution units, each working on a different stage of a different instruction. These CPUs can often execute more than once instruction per clock tick.
Larger numbers of execution units than two usually begin to see diminishing returns because of limitations on the speed of the computer memory. The only reason the larger numbers of execution units can be useful is because they are usually performing radically different services, and the microprcessor will often have a large on-chip cache.