We have some experience with these types of systems as well, and just like Grant said, it sound very much like a HTiB (Home Theater in a Box).
The very likely situation is that the subwoofer in your system is PASSIVE, meaning that the receiver itself powers it, as opposed to an ACTIVE subwoofer, where the sub has an amplifier on-board.
It is unlikely that you could just add another sub to your existing system, as the impedance of two subs in parallel wiring would probably cause problems.
One POTENTIAL option, and I caution against this, is adding a completely DIFFERENT passive subwoofer to the system, one with a larger woofer perhaps. The issues are impedance, power needs, and efficiency at that point.
So, going back to what Grant said, a new receiver with an ACTIVE subwoofer in the system will give you more flexibility in the future. HTiB’s weren’t meant to upgrade.