changing filtering "speed" (cutoff frequency) of an IIR filter knowing only its coefficients
Your probably your best option here is &quot;frequency warping&quot;. You can calculate the poles and zeros from the coefficients, warp the poles and zeros and then recalculate the coefficients again.
Warping is a procedure the applies a conformal mapping to the poles/zeros. Specifically a conformal mapping that maps the unit circle onto itself will maintain the overall shape of the filter but either bunch it up or stretch in the low frequencies (and vice versa in the high frequencies). A good choice is a first order allpass filter, that indeed maps the unit circle onto itself.
Loosely speaking you replace all delays in your filter with a first order all pass filter and recalculate the poles and zeros. That takes a bit of math to work out the details, but the actual code would be quite efficient.