First up, I-140s can again be filed in premium processing beginning Monday, June 1, 2020. Upgrades can also be done for I-140 petitions beginning Monday.
Next, beginning June 8th, pending H-1Bs that are cap-exempt, including transfers, extensions, amendments, and non-profit employers can be upgraded.
Also beginning June 8th, all other I-129s (i.e. L-1, TN, etc) that are pending can be upgraded.
Starting June 15th, initial H-1B filings for cap-exempt employers or Conrad/IGA waivers can be filed in premium processing.
Starting June 22nd, cap-subject H-1Bs that are pending can be upgraded and those that have not yet been filed can be filed in premium processing. Also, beginning June 22nd, all other I-129s can be filed in premium processing again.
All dates are subject to change as USCIS continues to take on more premium processing requests and USCIS will announce any changes to these dates accordingly.