I have an outdoor bench that came with instructions to coat it with teak oil once a year. I've done the teak oil one year so far. If I put on another coat of teak oil this year, do you think I can also put a clear-coat polyeurethane layer on top of that, once the teak cures and is ready for regular use?
First in case you don't know "teak oil", like "Danish oil", is just a marketing name for a finish various companies make. There's no legal definition of either name so what is in the container can literally be nearly anything each manufacturer decides to put in it. But generically, products sold under these names are oil finishes that are blends of oil with some varnish, then heavily diluted plus often with added drying agents so they dry reliably fast.
do you think I can also put a clear-coat polyeurethane layer on top of that, once the teak cures and is ready for regular use?
In principle, the answer is yes, you can successfully apply other finishes on top of wood that was previously treated with an oil or oil finish.
However, in this case it's likely not advisable.
As this is an exterior piece unless the other finish is specifically intended for exterior applications it shouldn't be used for that application. Interior finishes that aren't durable outdoors will readily break down and can discolour, go cloudy, crack or craze, peel or flake.
If you do want to apply a glossy clear finish to the bench the thing to use is a spar varnish or a marine varnish (the latter being more durable). But note these are all very strongly yellow/amber because of their high oil content and they impart that colouring to anything they're used on, as seen on most boat woodwork.
*As long as there isn't a film of the oil left on the surface of the wood (which there shouldn't be, with any finish of this kind all excess is intended to be wiped from the wood each time it's applied).