In this paper we consider a generalized k-server problem with parallel requests where several servers can also be located on one point (which was initiated by an operations research problem). In Section 4 the ''compound Harmonic algorithm'' for the generalized k-server problem is presented. Certain multi-step transition probabilities and absorbing probabilities are used by the compound Harmonic algorithm. For their computation one step of the generalized k-server problem is replaced by a number of steps of other (generalized) specific k-server problems. We show that this algorithm is competitive against an adaptive online adversary. In the case of unit distances the Harmonic algorithm and the compound Harmonic algorithm are identical.