I have a standar heat-cool system with a three speed fan motor. Whenever the system switch is moved to "heat" the furnace fan motor should run constantly at low speed.
Adotionally, as the fan switch closes during the heating cycle it should change the fan speed to medium. Finally, the fan must still attain high speed for air conditioning.

I have achieved this with two aditional relays (there's one already in the system); but the challenge now is to make it work with only one aditional relay.

Normally in the heat mode the motor will run in a slower speed than when on A.C. but when the thermostat is satisfied the blower will run for ninety seconds or so and stop completely. Then when the thermostat calls for AC the motor runs on high.

How many wires do you have that go from the control box down to the motor.

Use a double pole double throw relay to replace the two you added