Other time-frequency-plane tiling than STFT, DWT, ConstantQ-Transform: multiresolution STFT?
Your time-frequency grid is Mondrian-shaped: essentially, rectangles supported on dyadic splits of the time or the frequency axes. Hence, you can easily start for any reversible time-frequency tiling, and further slit any of its rectangle onto another invertible tiling. Some call that hierarchical, or nested time-scale/time-frequency decompositions. As long as each is invertible, the combination remains revertible. 

Furthermore, dyadic and power-of-two uniform decompositions can be turned into the other, only by grouping coefficients. This was used for instance in A DCT-based embedded image coder, 1996: an eight (or $2^3$) multiband filter-bank DCT was turned into a 3-level dyadic structure.

So, combining dyadic wavelets and $2^K$ windowed filter-bank, you can get invertible schemes as wished.

One issue though: how does one choose how to nest those different embedded decompositions? Seen as wavelet or local cosine, lapped-transform packets, entropy concepts could be used, but the diversity can be huge.