The changes would not go into effect until the court lifts its injunction.
Houston and Philadelphia were among the major cities where sweeps of 300,000 mail-in ballots were made.
RECORD EARLY VOTING: Election Day is just days away and already more than 75 million Americans, including nearly 8 million Californians, have voted either in-person or through mail-in ballots.
'HISTORIC' NUMBERS: By this time in 2016, only 150,000 Californians had turned in their mail-in ballots compared to 1.5 million this year, about three weeks out from Election Day.
Ballot requests in 38 states, whether by mail or through some form of in-person early voting, surpassed 35 million this week.
Abbott's order shuttered dozens of sites statewide, limiting the number of drop-off locations to one per county, including in Texas' biggest cities.
