Situation:

Dr. Strange
Clea - Compel
Assorted SHIELD agents

When Dr.Strange takes an action, he uses Perplex, Clea's Enhancement, and the SHIELD ability to boost up his attack/range/damage.

Then, Clea Compelsthe Doctor to attack again.

Question: Does he retain the bonuses he receives from the SHIELD agents?

I can't find anything in the rules that says they don't retain the bonuses so I'd say they do. I think the intention was for the duration of the attack, but they may last until the end of the turn. The team ability doesn't say when the bonuses go away nor does the player's guide.

Posting in the Judges forum to find out.

I'm no judge, but I would say you at least wouldn't get the damage part as you use the power action for the ranged attack.

Remember to use the Defenders TA to lower Doc's Defense to help in the compelling.

Just thought I'd offer that just in case, since I have no answer to your actual question...

I would think that SHIELD +damage would not last. Since you have to specifically give the SHIELD an action and a token immediately before the shot, then I'd say you would lose the bonus after the shot.

As for the SHIELD +range, I'd also say that it wouldn't last (for the same reasons) But since is free, you could do it a second time for the second attack. You could even SHIELD up +range for the first attack and +damage for the second or vise-versa.

Yes, the shield damage doesn't specify when it ends, but because they're given an action to perform it, it can be assumed it's restored to default at the end of the action.
Enhancement is free and can be used as many times during a turn as you want (But only once per character per attack). And the shield range bonus can be used once per attack too.

Remember to pack a hydra to wildcard to for +1 attack per character

Page 6:

"Modifiers and replacement values that take effect during an action
are in effect only for the duration of that action unless stated otherwise.
Modifiers and replacement values that take effect during an attack are in
effect only for the duration of that attack unless stated otherwise. When
a value would be both replaced and modified, replace the value and then
modify it."

Thanks, Harp. That's the answer we're looking for.