AMPL Group Qualified Assignment How to Fix Problem - variable-assignment

Question

set student;
set group;
var assign{i in student, j in group} binary;
param pref{i in student, j in group};
maximize totalPref:
sum{i in student, j in group} pref[i,j]*assign[i,j];
subject to exactly_one_group {i in student}:
sum {j in group} assign[i,j] =1;
subject to min3{j in group}:
sum{i in student} assign[i,j]>=3;
subject to max4{j in group}:
sum{i in student} assign[i,j]<=4;
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data;
set group:= A ED EZ G H1 H2 RB SC;
set student:= Allen Black Chung Clark Conners Cumming Demming Eng Farmer Forest Goodman Harris Holmes Johnson Knorr Manheim Morris Nathan Neuman Patrick Rollins Schuman Silver Stein Stock Truman Wolman Young;
param pref:
A ED EZ G H1 H2 RB SC:=
Allen 1 3 4 7 7 5 2 6
Black 6 4 3 5 5 7 1
Chung 6 2 3 1 1 7 5 4
Clark 7 6 1 2 2 3 5 4
Conners 7 6 1 3 3 4 5 2
Cumming 6 7 4 2 2 3 5 1
Demming 2 5 4 6 6 1 3 7
Eng 4 7 2 1 1 6 3 5
Farmer 7 6 5 2 2 1 3 4
Forest 6 7 2 5 5 1 3 4
Goodman 7 6 2 4 4 5 1 3
Harris 4 7 5 3 3 1 2 6
Holmes 6 7 4 2 2 3 5 1
Johnson 7 2 4 6 6 5 3 1
Knorr 7 4 1 2 2 5 6 3
Manheim 4 7 2 1 1 3 6 5
Morris 7 5 4 6 6 3 1 2
Nathan 4 7 5 6 6 3 1 2
Neuman 7 5 4 6 6 3 1 2
Patrick 1 7 5 4 4 2 3 6
Rollins 6 2 3 1 1 7 5 4
Schuman 4 7 3 5 5 1 2 6
Silver 4 7 3 1 1 2 5 6
Stein 6 4 2 5 5 7 1 3
Stock 5 2 1 6 6 7 4 3
Truman 6 3 2 7 7 5 1 4
Wolman 6 7 4 2 2 3 5 1
Young 1 3 4 7 7 6 2 5;
Suppose that you are allowed to assign up to two groups to un-qualified students. How would you reformulate the problem and find the new solution, with preference still applying? * means un-qualified
param pref: A ED EZ G H1 H2 RB SC:= Allen 1 3 * 7 7 5 * 6 Black 6 * 3 5 5 * 1 3 Chung 6 2 3 1 * 7 5 * Clark * 6 1 * 2 3 5 4 Conners 7 6 1 3 3 * * 2