You can have a group assignment and still provide separate grades to group members. Just use the Assign Grades to Each Student Individually setting when you edit the assignment. With this setting unchecked (the default), grades will automatically be set for all group members as soon as you enter a grade for one member. With this setting checked, you will be able to change grades on a student-by-student basis.
This setting can be applied when you create the assignment, or it can be applied later. Therefore, if most students will receive the same grade as their team members with a few exceptions, you can save time by leaving this setting off, setting your group grades, and then turning this setting on and making your adjustments. If you do this, you may want to mute the assignment while you are changing grades so that students are not surprised.