1-10Hz frequency count translated to PWM for stepper motor RPM
You could try using a PLL (Phase-locked loop). The idea is to put a digital divider equal to the desired multiplication factor in the feedback loop. In your example, it would be a divide by 10.
You could generate a higher frequency to allow more granularity in the division, for example, generate some digitally variable number like 100x the input frequency, and divide that by a fixed 10 for the output. Then you could select 99/10 = 9.9 times the input frequency.
It won't respond as quickly as a microcontroller circuit that could precisely measure the time between input edges and generate a resulting output frequency, and it could overshoot or be excessively sluggish responding to input changes, depending on how you design the filter.
An example PLL is the CD4046 (1970s technology).