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)

Relevant cards

Note: All applicable cards may not be listed below.
SM10_178
SM10_178