The EXACT= option imposes a constraint on the matching that limits the feasibility of what matched sets can be produced, so it is not really appropriate to say more than one matching is occurring. In particular, EXACT= option requires all observations in a matched set to have the same value(s) for the categorical variable(s) listed in the option.
If you are performing a greedy matching with the EXACT= option specified, this constraint means that when the procedure looks for the nearest neighbors of a given treated unit, it only considers the observations in the control condition that have the same value(s) of the variable(s) listed in the EXACT= option.
If you are performing an optimal matching method, the constraint imposed by the EXACT= option becomes a constraint for the underlying optimization problem that is solved to create the matched sets, and again limits the feasibility of what observations can be matched together.
