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Probably it is possible to operate at the edge of the threshold voltage, but deep sub-threshold is not recommended becasue of worse matching between the circuit and the output current mirror. Question is how much area you have, do you have a limit?
Stacked diodes are not too good (Mp1 and Mp2) in any design, rather use 1 diode and solve the cascode output with extra circuitry. I mean keep the output cascode device (Mp6) and generate its bias voltage with other current mirrors + PMOS diode, which mirrors aren't cascoded. It would help a lot on spare drain-source voltages and designed device Vdsat voltages could be higher.