Designing schmitt trigger having two positive thresholds
The standard Schmitt trigger circuit makes it difficult to apply variable upper and lower threshold voltages that are independent of each other so, start by creating two threshold voltages using independent resistive potential dividers.

Next use two comparators both fed with the common input signal but whose reference voltages are from one or the other threshold voltages. Finally, use a D type flip-flop where the upper threshold comparator feeds the clock pin and the lower threshold comparator feeds the reset pin. The D pin is fed with logical 1. Output is taken from the nQ output of the flip-flop.

This works because I've used it and is pretty similar to what happens inside a 555 timer: -



If you had access to the non-inverting pin of comparator 2 then you could use a 555 chip; trigger and threshold would be tied together and connected to the input. Upper voltage threshold would connect to "control voltage" and lower threshold would connect to comparator two's non-inverting input.