I wouldn't do it. Best to replace one of the speakers so they match. In general, 2 16 ohm cabs, set to 8, 2 8 ohm cabs, set to 4.
Mathematically, it doesn't need to match - the amp won't care, it will just see a combined load of roughly 5.3 ohms, as calculated by
@andy474x .
Imagine, if you will, that the 8 ohm cabinet really has two 16 ohm speakers wired in parallel inside, resulting in a net 8 ohm impedance. By then also connecting the 16 ohm 1x12 cab in parallel, the amp "sees" three speakers in parallel, all 16 ohm, or 5.3 ohms net. The safest setting for the amp would be the 4 ohm setting. (I actually asked PRS about this very situation, adding a 2x12 cab at 8 ohms to an existing 1x12 combo with 16 ohm speaker.)
In the case of the OP, mixing an 8 ohm speaker with a 16 ohm speaker, the speakers will naturally behave a bit differently in the two cabinets due to their different impedances, but maybe that will result in a more desirable tone, overall.
However, me being the "optimize if possible" type, would prefer to use speakers all of the same impedance individually, wired in parallel, such that the amp sees "exactly" 4 or 8 or 16 ohms. (I realize the speakers are never truly exactly a certain impedance, it will vary by frequency and probably a few other minor factors).