Can I eFile federal return now, and seek extension for my 3 states? (MN, CA, NY)

Yes, you can, but Minnesota and California automatically grant a 6-month extension to October 15.

For New York information, please see the TurboTax FAQ "Do I need to file a state extension? If so, how do I do this?" below for guidance.

https://ttlc.intuit.com/replies/3300227