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)

Relevant cards

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