Multiband undersampling
I found the answer in Akos, D.M., Stockmaster, M., Tsui, J.B., &amp; Caschera, J. (1999). Direct bandpass sampling of multiple distinct RF signals. IEEE Trans. Communications, 47, 983-988.

The extra condition between the 2 bands is: $|F_{IF1} - F_{IF2}| &gt;= \frac{BW_{I1} + BW_{I2}}{2}$ where $F_{IF}$ is the intermediate frequency and $BW$ the bandwidth.

There are then 4 equations that describe all these constraints (eq $(1)$ to $(4)$) in the paper. Unfortunately, the first constraint contains a non-linear combination which cannot be solved analytically (by something like mixed-integer programming).

This is confirm in the paper: "An iterative procedure, based on these equations, was developed to determine sampling frequencies that would meet the requirement, the results of which are displayed in Fig. 5.". I conclude there is no better solution than iteratively going through the frequencies under consideration.