  We say that a graph F strongly arrows a pair of graphs (G,H) if any colouring
of its edges with red and blue leads to either a red G or a blue H appearing as
induced subgraphs of F. The induced Ramsey number, IR(G,H) is defined as the
smallest order of a graph that strongly arrows (G,H). We consider the
connection between the induced Ramsey number for a pair of two connected graphs
IR(G,H) and the induced Ramsey number for multiple copies of these graphs
IR(sG,tH), where xG denotes the pairwise vertex-disjoint union of x copies of
G. It is easy to see that if F strongly arrow (G,H), then (s+t-1)F strongly
arrows (sG, tH). This implies that IR(sG, tH) is at most (s+t-1)IR(G,H). For
all known results on induced Ramsey numbers for multiple copies, the inequality
above holds as equality. We show that there are infinite classes of graphs for
which the inequality above is strict and moreover, IR(sG, tH) could be
arbitrarily smaller than (s+t-1)IR(G,H). On the other hand, we provide further
examples of classes of graphs for which the inequality above holds as equality.
