In general, this is permitted in circumstances where you have the time and authorization (a visa, for instance) to exit the airport. In such cases, you can simply approach the check-in counter at the airport, as if you were beginning your journey at your layover airport, and check a bag at this stage. Normal checked bag limits will apply, so if you exceed your allowance by checking (additional) luggage during a layover, you will be charged normal excess luggage fees.
In situations where you do not leave the airport, whether you can check additional luggage may depend on the airline in question, and possibly even the airport. In some cases it is possible to gate check luggage on to your final destination.
In practically all cases, the airline will have some contingency plan in place for passengers who arrive at the gate with luggage in excess of the carry-on allowance. Such contingencies may incur excess fees (perhaps much higher than the normal checked bag fee). If you will find yourself having to check additional luggage at the gate, your best bet is to check with the airline about your specific flight plans, to see what the options are for you.