Depends on the card.
Some relay output cards are isolated relay outputs - that is, each output has two connections, one for each side of the relay.
Others simply have a single common for all relay outputs and then each output has a single connection for the other side of the relay.
Others still are split into two isolated groups, with two commons, each serving half the output relays. Based on your description, I'd hazard a guess that this is they type of card you have, but you don't specify or provide any part numbers, so it's best to spell it all out to be sure.
If you do have the latter type of output card (or the first type - just not the second), then yes, you could do it. But "could" is not really a ringing endorsement. I've never seen it done before either, and would not do it myself unless I really had no other choice. The risks of a mistake during wiring/troubleshooting/etc, and the consequences thereof, are just too high. You can do it. But personally, I wouldn't.
I've put it like this before: there's no law against riding an electric scooter down a waterslide.