Gurobi mixed integer linear programming backend for SageMath. Source repository for https://pypi.org/project/sage-numerical-backends-gurobi/, can be installed on top of distributions providing SageMath. See also https://github.com/sagemath/sage-numerical-backends-cplex and https://github.com/sagemath/sage-numerical-backends-coin
Gurobi supports computing multiple solutions (solution pool) to the problem as explained at https://www.gurobi.com/documentation/9.5/refman/finding_multiple_solutions.html but currently there is no way to retrieve them in Sage.
Corresponding Sage ticket: https://github.com/sagemath/sage/issues/34183