Premiership Rugby has moved two fixtures in mid-May to a Monday night in the hope of having fans attend.
Newcastle Falcons' game with Northampton Saints at Kingston Park and Gloucester's visit to Bristol Bears have been moved to Monday, 17 May.
Under the UK Government's Covid-19 roadmap crowds of 50% capacity up to a limit of 4,000 may be able to attend matches from 17 May.
Premiership Rugby will make decisions on three more games at a later date.
Wasps are still scheduled to host Worcester behind closed doors on Saturday, 15 May, while a decision on London Irish's game with Exeter will be made once landlords Brentford know if and when they will play in football's Championship play-offs.
A decision on Bath v Sale and Leicester v Harlequins will be made once both hosts have played their European Challenge Cup semi-finals.
Should either make the final, which is the following weekend, their games will not be moved in order to give them sufficient time to rest and recover.
The first rugby match to have a crowd in the British Isles in 2021 takes place on Saturday when Championship side Jersey Reds welcome 1,000 fans for their game with Nottingham after approval from the island's government.
Three Premiership games in December had crowds of up to 2,000 during a temporary easing of Covid-19 restrictions late last year.
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