  Bergstra and Klop have shown that bisimilarity has a finite equational
axiomatisation over ACP/CCS extended with the binary left and communication
merge operators. Moller proved that auxiliary operators are necessary to obtain
a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that
this remains true when Hennessy's merge is added to that language. These
results raise the question of whether there is one auxiliary binary operator
whose addition to CCS leads to a finite axiomatisation of bisimilarity. We
contribute to answering this question in the simplified setting of the
recursion-, relabelling-, and restriction-free fragment of CCS. We formulate
three natural assumptions pertaining to the operational semantics of auxiliary
operators and their relationship to parallel composition, and prove that an
auxiliary binary operator facilitating a finite axiomatisation of bisimilarity
in the simplified setting cannot satisfy all three assumptions.
