MLS teams adjust to a summer of soccer without some of the league’s biggest names

Lionel Messi could miss as many as six games with Inter Miami if Argentina wins its way to the Copa America final.

With 12 goals and a league-leading 13 assists, Messi has helped push Miami to the top of Major League Soccer’s Eastern Conference. Questions loom about whether Miami can weather his absence during the Copa America, which starts on Thursday.

But it’s not just the eight-time Ballon d’Or winner who will be missed.

Inter Miami also will be without Luis Suarez, who...