The Miami Marlins on Thursday had another player test positive for the coronavirus, bringing the team's total to 19, a source confirmed to ESPN.

In all, the Marlins have had 17 players and two coaches test positive over the past week, sources confirmed to ESPN. All games for the team have been postponed through Sunday by Major League Baseball.

The team is assessing how to fill out a roster with a combination of players: those already in the organization and training at its alternate site in Jupiter, Florida; free agents; and waiver-wire claims.

Switch pitcher Pat Venditte, who who was with the Marlins during spring training, agreed to a minor league deal with the team on Thursday, his agent, Marc Kligman, told ESPN. He could join big league club soon.

Starting pitchers Jose Urena and Sandy Alcantara, first baseman Garrett Cooper, right fielder Harold Ramirez and catcher Jorge Alfaro are just some of the players who have tested positive for coronavirus.

The Marlins remain in Philadelphia, where they played last weekend and have been undergoing daily testing. The prospect of the team's season restarting Tuesday at home against the Phillies remains in question.

If, instead, the Marlins play that series in Philadelphia, they could bus to New York to face the Mets, then bus to Buffalo, New York, where the Blue Jays plan to play their home games this season. In that scenario, the Marlins would not return home until their Aug. 14 series against Atlanta, though Miami-Dade County currently requires a 14-day quarantine for people coming into the area from New York, further complicating matters.

Miami could make up the three games against Washington that have been postponed this weekend by scheduling two doubleheaders during future series and playing on their shared Sept. 17 off day. How to make up the four lost games against Baltimore, an interleague opponent, could prove tricky, leading to the possibility the Marlins won't play a full 60-game schedule.

In light of the Marlins' outbreak, MLB is encouraging players not to leave hotels in road cities except for games, mandating the use of surgical masks instead of cloth masks during travel and requiring every team to travel with a compliance officer who ensures players and staff properly follow the league's protocol, sources told ESPN on Wednesday.

ESPN's Jeff Passan contributed to this report.