That can definitely be done, no need to purchase a net new license.
There are different costs, however, depending if your license is currently node-locked (tied to a single workstation), or floating (LAL license, which can be situated on a server).
The upgrade costs are below:
Core (Node-Locked) to FX (Node-locked) = $2,695
Core LAL (floating) to FX LAL (floating) = $4,195
So it looks like it costs a little more overall, but you're able to spread out the cost if your end goal is an FX license