If I move Vex into a battlefield which has an enemy Overzealous Fan, and he activates his ability to send Vex back to base, can I still play discounted spells before the chain ends?

To answer your question: No, you cannot play additional spells while the chain is resolving.

Here is the breakdown of why this is the case, based on the rules of Riftbound:

The Sequence of Events

1. Vex enters the battlefield: When you move Vex into the battlefield, she enters the board. If this initiates combat, any "When I Attack" or "When I Defend" triggers are placed on the chain.
2. Overzealous Fan's Trigger: Overzealous Fan has a triggered ability ("When I defend..."). When you move Vex into the battlefield to attack, this trigger is placed on the chain.
3. The Chain is Closed: Once the trigger is on the chain, the state becomes CLOSED. In a closed state, you cannot play [ACTION] spells. You may only play [REACTION] spells.
4. Resolution: The chain resolves in LIFO (Last-In, First-Out) order. The Overzealous Fan's ability resolves, moving Vex to your base.
5. State Returns to Open: Only after the chain is completely empty does the state return to OPEN. At that point, you regain priority and focus, and you would be able to play new spells.

Why you cannot play discounted spells "before the chain ends"

• Rule 154.3: "While a spell or ability on the chain is Resolving, no other spells or abilities can be finalized on the chain or resolved..."
• Rule 336.1: "The newest item on the Chain resolves. Execute its game effects in their entirety."
• Timing: Because Overzealous Fan's ability is a triggered ability that uses the chain, it must fully resolve before the chain is empty. You cannot interrupt the resolution of an ability to play a new spell.

Summary: You must wait for the chain to finish resolving and for the state to return to OPEN before you can play any new spells. By the time the state is open again, Vex will already be at your base, meaning she is no longer in combat, and her ability (which only functions while she is in combat) will no longer be active to provide any discounts.