ASUS is the only mfgr I could find that makes a 32" monitor with PIP; so, my options are limited. Granted, I am nowhere near ready to buy one, but ASUS' ones have a dumb placement of the controls: on the rear! With the same layout, I imagine frequently pressing the power button instead of the input select.
You could buy a 4K 32" LCD HD TV and use that as a monitor. Most Televisions have the PIP feature. The disadvantage of using the TV would that you'd have to buy a stand for it, as monitors sold for computer use have stands that allow for tilt and pan, while TV sets usually come with a simple "foot". The price for the TV set would probably be LESS than the monitor, TV's usually DON'T have display port or DVI inputs, but both are compatible with HDMI if you get the right cables.