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Solid state final amplifiers need to be followed by a low pass filter to take care of harmonics. (Back in the days of tubes, most radios used a final with a tuned tank circuit that acted as a bandpass filter. That kind of circuit is harder to design in the low voltage / high current world of transistors, plus people want the convenience of a no-tune design, so solid state rigs are not designed that way.) In a multiband rig the lowpass filters have to be switched for each band. In the QCX design, the low pass filter is inductors L1, L2, and L3, and the associated capacitors C25, C26, C27, and C28.

Most solid state final amplifiers are broadband, but the QCX uses a Class E final. A Class E final is inherently narrowband, as it depends on resonance in the tank circuit for its operation. In the QCX design, inductor L4 and capacitor C30 are the relevant components.

Finally, there is a bandpass filter in the receiver circuit. (It's not in the circuit when you transmit.) The components involved are transformer T1 (which also acts as part of the phase splitter), and capacitors C1, C5, and C8. C5 and C8 are not installed on some bands; those three capacitors are in parallel and need to add up to a suitable value of capacitance for the band. The amount of inductance also varies, as T1 is wound differently depending on the band.

Band switching the QCX is more involved than it would be for a typical solid state design. The Class E final means there are additional parts that would have to be switched to achieve Class E operation on each band. The way that the bandpass filter and phase splitter are combined is a very efficient design for a single band rig, but converting it for multiband operation would be difficult. It would likely be better to switch to a different circuit topology rather than try to switch all the components in the QCX. Another approach would be to use plug-in band modules, as some versions of the uSDX do; that can work well, but it makes changing bands more involved than just pushing a button on the front panel.