The default gateway is the route use if none of the other routes match. So by that definition, there can be only one at a time.
Except not really, because your routing rules might be more complicated. Modern versions of Linux, for example, support using multiple completely independent routing tables, and making packet-by-packet determination as to which table to consult. So for example, perhaps you have one network configuration used for normal traffic, but a completely different routing table for your web browser. Or perhaps you have another routing table that's only used for packets with specific TOS bits set. But each would have its own default gateway which would reflect the default route for that specific routing table.
Normally, the routing table is as simple as, "local traffic to the local interface, everything else to the router." But if you're using a more complicated network setup, then the tools exist to cope with whatever network scenario you can dream up.