if i understood right the answer is there are specific antibodies are produced against specific antigens (vaccine) it doesn't matter if it is in combination or single, the response can be differenciated ....generally it is determined by serial dilution method
vaccines if administered properly will produce almost the same effect irrespective of whether given singly or in combination. however the cost of giving singly may be higher than combined multi-combined (storage, transport, personnel cost, time. however untoward effects (pain, fever) may be higher with combined vaccines.
a proxy will be to look at recipients view and what will stop them from receiving the vaccine.