Combining spectrograms with different windows to getting arbitrary time and frequency resolution
Improving the time/frequency resolution balance remains a standard research issue, trying to adapt the STFT, inventing novel/better time-frequency distributions (Wigner, Cohen), using together or combining the above. For instance in music or speech source separation, a couple of STFTs is often used with both short and long windows, to be able to separate   transient from larger signals.

The ways you can combine such SFTF depend a lot on the exact processing or features you want to extract, as detailed by @hotpaw2. Here are a few pointers to references suggesting methods. The first one suggests a point-wise combination of two spectrograms as $$S_c(f,t) = (|S_1(f,t)||S_2(f,t)|)^{1/2},$$ and the second generalizes it to the geometric mean, the minimax or the reciprocal average.  The third encompasses it in a more generic merging approach.


Combined multi-resolution (wideband/narrowband) spectrogram, ICASSP 1991
On Combining Evolutionary Spectral Estimates, 1994
Adaptive Time-Frequency Resolution for Analysis and Processing of Audio, AES 2006