If (R) Hawkeye is carrying Dr.Doom (both from Fan Forces) during a Move and Attack, and the Thunderbolts card was used to give Hawkeye the Syn Sindicate TA, than Hawkeye's Attack is 9 (Doom's 11 -2) not 7 (Hawkeye's own 9 -2), correct?

No. The Transporter move and attack ability works like HSS option 1. During the move action, Dr. Doom is effectively off the board, even during the free attack since that occurs *during* the movement. If Dr. Doom isn't on the board, he can't share his AV with Hawkeye.

But it could work to perplex up Hawkeye's ATK prior to the move and attack?

Sure. In fact, you could Perplex it up a total of 5 times since the -2 to to AV (due to the move and attack) would bring that down to a net +3 (which is within the Rule of 3).

Thank you, sir!
Appreciate the quick feedback.

I'm pretty sure the Rule of 3 prohibits a value from being modified more than 3 times.

Subtracting it by 2 and then adding 3 would be modifying it 5 times.

The best you can do is subtract 2 and add 1 for a total modification of 3.

From the Universe Rule Book:
Rule of 3
Many modifi ers can affect combat values during the game. Because all modifiers are cumulative, there is a special rule called the rule of 3. The rule of 3 states
that once all modifiers have been calculated, no value can be modified by more than 3. It is important to note that the effects of powers and abilities and team abilities override standard HeroClix rules. The rule of 3, however, takes precedence over any powers and abilities and team abilities.

So, if you take a -2 penalty due to move-attack-move and add +5 bonus from 5 Perplex free actions, all of the modifiers add up to +3.