Spectrograms convert an amplitude-time signal into a frequency-time signal using Short Time Fourier Transform (STFT). The window size L used in STFT is a design choice. As L increases, you get higher frequency resolution and lower time resolution and vice versa.
If you performed STFT with a large L to get spectrogram A with high frequency resolution then performed STFT with small L to get spectrogram B with high temporal resolution, can you combine spectrogram A and B somehow to get high temporal and frequency resolution?
My gut feeling is no, as changing L is simply "changing how you interpret the amplitude-time data."