TS334IPT has open drain outputs but I'm not sure how high the outputs can be pulled. My interpretation of the datasheet is that the max output voltage is 5.5V independent of the supply voltage. But perhaps the max output voltage is dependent on the supply voltage, that is the max output voltage is equal to the supply voltage?
I want to pull one of the outputs to 5V using a supply voltage of about 3.6V. Is that safe?

TS334IPT datasheet

 

I can see no reference to the output voltage able to be higher than the supply voltage so I don't think that would be safe.

 

It has NO "Output Voltage", the Output "Sinks Current",
so use it as designed, with a "pull-up" Resistor attached to its Supply Voltage.
There is no internal schematic in the Data Sheet, so apply more Voltage at you own risk.
Then simply attach a "Level-Shifting" Buffer, or
a small "Logic-Level" FET, with a Vds rated for any Voltage you like.
Keep in mind the Gate Capacitance of the FET, as it could limit how high you can go in frequency
.
.

 

I want to pull one of the outputs to 5V using a supply voltage of about 3.6V. Is that safe?

The maximum output voltage is 5.5V, and since that's a drain, it should tolerate that voltage independent of the comparator's supply voltage.
So using an output pull-resistor to 5V with the comparator operating at 3.6V should be fine.

Note that the TS334IPT is a comparator, not an op amp.