controlling 3 relays with 1 signal wire
Satellite dish receiver LNB units do exactly this by sensing the  DC bias voltage on the coax line. This approach could be adapted for your purpose.

This would require two comparators and some simple gating. It would work as follows.

Set the comparators at Vth(1) and Vth(2). Assume Vth(1) is less than Vth(2). Vbias is the control voltage. Then:

Vbias &lt; Vth(1): Turn on Relay 1
Vbias &gt; Vth(1) and &lt; Vth(2): Turn on Relay 2
Vbias &gt; Vth(2): Turn on Relay 3


If you need the 4th state of all relays off, add another comparator, set to Vth(0) some value less than Vth(1). The table becomes then:

Vbias &lt; Vth(0): all off
Vbias &gt; Vth(0) and &lt; Vth(1): Turn on Relay 1
Vbias &gt; Vth(1) and &lt; Vth(2): Turn on Relay 2
Vbias &gt; Vth(2): Turn on Relay 3


There are specialty chips for satellite set-tops to make the bias voltage, but in your case a simple LDO with a couple of settings should do it.