No. But the limitation of 2 Master-Details has no effect on the number of Many to Many relationships an object to have.
1) You can use lookups to accomplish the exact same thing as a Master-Detail if the only requirement is to have a Many to Many relationship.
2) The limitation of 2 Master-Details per object has no effect on the number of Many to Many relationships that use Master-Detail. In a Many to Many, the Master-Detail relationships goes on the child junction object not the parent object itself. That means all you need to do is create more junction objects (which is what makes the object many to many), with each having the maximum of two Master-Detail relationship fields.
Account <- -> Contact: Junction of AccountContactRole to create a Many to Many relationship
Account <- -> Special_Asset__c: Junction object of AccountAssetType__c to create Many to Many relationship
Account <- -> Case: Junction of AccountCaseLink__c to create a 3rd Many to many relationship.
You now have 3 junctions that all use Master-Detail to create Many to Many relationships. (Keep in mind that these are Theoretical objects I am using here and so likely make no sense in your org past my example.)