Can I fast cast spells intentionally after the opponent goes but before the round ends?
If I can't can I cast an enrage spell on Sleepy the Grog, he who always botches initiative, and then cast group target spells at other targets?
Do you mean that your mage has had his/her action, the opponent has had his/her action, but before some other character has their action?
I don't have my books in front of me, but I seem to recall that you should be able to attempt to Fast Cast before the actions of a particular character. How much Fast Casting per round you can do I would need to look up.
But if there is no other characters to perform actions before the round ends, I would think you are asking to Fast Cast at the beginning of the next round.
In my group's interpretation, Fast-Casting is only as a reaction to some attack or action taken towards you. We want to avoid situations where a magus abuses it when an opponent picks his nose (or something else irrelevant) for an excuse to cast another Pilum of Fire.
So, as we see it - and want it to work - you can't use fast-casting to time an extra action.
However, if you use the initiative and timing rules from Lords of Men I'd happily accept a Delayed action to wait for someone else to do something before you take your own action. Or an Interrupt, to do it before - however this requires an Action Priority Roll.
I believe you're the person mainly worried about it though 