Godzilla: Tokyo SOS

Another direct sequel that follows completely different human characters. Made by the same director, who also helped write this time around, and a new effects director.
 

Godzilla X Mechagodzilla AKA Godzilla Against Mechagodzilla

After GMK was a success, but Kaneko did not want to return, Toho turned back to Masaaki Tezuka and decided it was time to bring back a new version of Mechagodzilla.

Godzilla X Megagauirus

Unlike the Heisei films that were connected in one way or another, most of the films in the Millennium series are stand alone with there own backstories. Although they usually referenced back to the original 1954 Godzilla. This time we have a alternate history where Japan has no nuclear power and has moved the capital to Osaka.