An Input/Output Automaton is an automaton with a finite number of states where each transition is associated with a single inpuf or output interaction. In [1], we introduced a new formalism, in which each transition is associated with a bipartite partially ordered set made of concurrent inputs followed by concurrent outputs. In this paper, we generalize this model to Partial Order Input/Output Automata (POIOA), in which each transition is associated with an almost arbitrary partially ordered set of inputs and outputs. This formalism can be seen as High-Level Messages Sequence Charts with inputs and outputs and allows for the specification of concurrency between inputs and outputs in a very general, direct and concise way. We give a formal definition of this framework, and define several conformance relations for comparing system specifications expressed in this formalism. Then we show how to derive a test suite that guarantees to detect faults defined by a POIOA-specific fault model: missing output faults, unspecified output faults, weaker precondition faults, stronger precondition faults and transfer faults.