control multiple inputs with one potentiometer
Building a polysynth is quite a bit different chore from building a monosynth. Don't expect you can simply just take a mono synth voice, replicate that n times, and somehow magically wire them up as a polysynth.

The trick is that the voice has to be entirely voltage controlled, including all the static parameters that in a mono synth would be controlled by a simple potentiometer or a switch (switches would usually be replaced by a 4053 analog switch or a more modern equivalent). Then you use a microcontroller to generate control voltages and switch signals for the voices, and to read the keyboard, MIDI, digitize the front panel potentiometers and so on. As a free side-effect it's now quite trivial to implement patch storage on the micro.

If you do that naively, for \$k\$ analog parameters and \$n\$ voices you need \$kn\$ DAC channels, plus a bunch of digital outputs for the switches. As even a simple synth voice can easily have 20 parameters, for 8 voices you'd need 160 DAC channels! So the first thing you do is that you of course use just one channel to feed all of the parameters that are identical between voices (typically everything else except pitch control and envelope gates). This is why analog polys are typically not fully multitimbral. The second thing is that you use an analog multiplexer and sample-and-hold (such as a 4052, a hold cap and an opamp buffer) to generate the control voltages (if you're hand building a one-off instead of a commercial product, you might want to just splash out for a lot of multichannel SPI DAC's though, just to save up on soldering at the expense of a lot higher component cost).

By the way, you can probably see at this stage that writing the software for the microcontroller is not a completely trivial task...

In the modern day and age, your biggest challenge in the analog sense is to have an ADSR where the A, D, S, and R are all voltage controlled, without using a huge number of components per voice. Most modern polys solve this by having digital envelopes (but then this means that there's a DAC channel per voice for each of the envelopes, since their output will typically be different), whereas older polys typically had an ADSR IC. As it happens, such an IC is again in production, though it's not cheap: AS3310.

The details on how to do the multiplexing, converting typical monosynth circuits to complete voltage control and so on, are way too long for a EE.SE answer. However, you can get the idea, and a lot of inspiration, by studying the service manuals of the old classics, containing full schematics, many of which are readily found on google. Out of the really big names, at least the OB-Xa and Jupiter 8 schematics are immediately available. Note though that much of the details of the computer control can be done much easier today, since back then microcontrollers with integrated everything didn't yet really exist, so don't try to slavishly copy everything in these manuals.

So, to sum up: if you want to build a poly, you're signing up for quite a lot more than just replicating monosynth voices. However, it is a rewarding task, and if you want to pursue it I wish you the best of luck (and I, for one, would be interested in reading about your progress on a blog or such, if you're so inclined)!