Yes, you can leave the filter in the stock location, and add another one in series with a cooler.
That being said, why would you? Modern equipment is good enough that it's not necessary. And, it will increase resistance through the system - which is not a good thing.
You only need a
oil cooler if you're racing on a road course. For street driving, the
oil will not get Ot enough to perform like it should. So as weight, complexity, cost, and leak points. Really not worth the hassle and cost.