Two new cases of coronavirus, in two separate clubs, were found after the last round of Premier League testing.
The tests were conducted on Tuesday, Thursday and Friday of last week, with 996 players and club staff tested in general.
Players or club officials who tested positive now isolate themselves for a period of seven days.
This time, the tests available for each club have been increased from 40 to 50.
On May 19, the Premier League announced that, in the first round, six had positive results in three clubs. This included Adrian Mariappa from Watford and Burnley's assistant manager, Ian Woan. A total of 748 players and club staff were tested between 17 and 18 May.
The squads began non-contact training from Tuesday.
The Premier League has been suspended since March 13 because of the coronavirus pandemic, with 92 games remaining.
Speaking on Friday, Premier League chief executive Richard Masters said the league was "as confident as possible" on how to restart in June.
Asked about the date on which the Premier League intended to return, Masters said he must be "flexible" and learn from the resumption of the Bundesliga.
On Saturday, the Spanish Prime Minister said La Liga may resume behind closed doors from 8 June.