Can I put an extender between two access points?

Can you do it? Sure. 

Should you do it? probably not. Unless  your wanting slow speeds and potential instabilities. 

Reason why is that standard extenders by their very nature drop throughput 50%. Reason is they have to send router----extender and then extender----device. And they can't do both at once. This causes speeds to drop 50% and latency to increase. Add going from an router----extender----to another access point/extender and that final one is operating at roughly 25% speed. 

And thats all based if they're getting 100% signal/speeds which they rarely do. 

You can setup dual band extenders using fastlane 2 mode. It dedicates one of the bands for router---extender and the other for extender----device/AP. Tends to have better latency but not always better speess. Problem with that is one of those bands is the 2.4ghz which is slow to start with. 

You might see better performance utilizing a triband extender as they dedicate one of their 5ghz chips just for router---extender communication. And then you'd connect your access point to the other band. I've seen it done before with success but I've also seen it fail miserably. Its kind a gimmicking it up.

I usually recommend people who are needing more than 1 extender (especially if they're daisy chaining) to move to an actual triband mesh system. Not a dual band but a triband. It is more stable, faster, and just works because there's a router controlling it.