Let's say I have an audio clip of $N$ samples. I want to describe every $10$ ms of audio with an FFT of size $1024$, without information bleeding over from other $10$ ms windows. Given that the sample rate of this audio clip is a standard $44100$, I can't do that with a regular FFT. A regular FFT would give me $441 / 2 = 220$ bins.
Is it possible to take many, many FFTs of differing sizes over different windows to infer a larger frequency resolution for a smaller timeframe? Let's say I take a $1024$-FFT for each sample range increasing by $t = 1$ (samples $0$ through $2047$, then samples $1$ through $2048$ and so on), then a bunch of $512$-FFTs, then a bunch of $256$-FFTs. Would this large dataset contain enough useful information to "subdivide" the bins of the smaller, $220$-FFT?