Nelson boarding one enemy ship through another

Could a ship be boarded from one side while its crew counter-boarded another ship from the other?

Yes. At the Battle of Cape St Vincent, Nelson captured one ship and then used it as the route to board a second enemy vessel.

An apparently unlikely boarding scenario occurred at the Battle of Cape St Vincent. After taking one enemy ship, Nelson's men fought onward from its deck when another ship came alongside to assist. The result was the capture of two ships in succession, showing how quickly close action could merge separate crews and hulls into one battlefield.