Trainers » Lt. Surge's Strategy
If I play Lt. Surge's Strategy first, can I then play a second (or third) Lt. Surge's Strategy to play more than 3 Supporters?
Nope, that doesn't work. The second Lt. Surge's Strategy does not add to the number of additional Supporter cards you can play, so you can't play the second one at all because you cannot play Trainer cards for no effect.
Source: Unbroken Bonds FAQ (2019-04-19), TPCi Rules Team (2019-05-09)
Trainers » Lt. Surge's Strategy
If I have already played a Supporter, can I then play Lt. Surge's Strategy since I would be able to play 3 Supporters in total?
No. You would have to play Lt. Surge's Strategy as your first Supporter in order to be able to play any additional Supporters during your turn.
Source: Unbroken Bonds FAQ (2019-04-19), TPCi Rules Team (2019-05-02)