I want to check a fare for the following routing LAX to MNL via HKG and TPE to LAX via HKG.

Does the site allow you to do this? I have taken a look and don't see how this is done.

Also was wondering if CX Leverage will allow me to add a non CX flight to the itinery (in above example MNL to TPE on CI airlines.

Yes it gives me a quote doing MNL to TPE via HKG, but I prefer not to have to come back to connect in HKG