How do I add more resolution / taps to an analog -> digital filter?
Doing a decent sounding audio reverb with IIR filters is difficult. You need way more poles that you can generate with a normal IIR structure and you need a way to do it efficiently.


There is a significant trade off between sound quality versus MIPS, memory, latency &amp; controllabilty
A good starting point is the original Schroeder reverb, which uses comb filters and warped allpass filters. See for example: https://ccrma.stanford.edu/~jos/pasp/Example_Schroeder_Reverberators.html
You want to get lots of poles cheaply. For example, wrapping  a feedback loop around a long delay will create lots of poles with just a single multiply + add.
Ideally the poles are randomly distributed and have no regularity to them. The simple Schroeder algortihm doesn't quite do this, so it tends to sound "ringy" or "metallic".
A better alternative are feedback delay networks. See for example https://ccrma.stanford.edu/~jos/pasp/FDN_Reverberation.html. These work by having multiple delay lines of different lengths with a feedback matrix: i.e. each delay is fed back into all delays. This creates a very large number of relatively low Q poles.
Finally you can dial in all the frequency dependencies and also add some early reflections as sparse FIR filters (with IIR frequency shaping on the spares tabs)