Satisfiability modulo theories (SMT) solvers rely on various quantifier instantiation strategies to support first- and higher-order logic. We introduce MBQI-Enum, an approach that extends model-based quantifier instantiation (MBQI) with syntax-guided synthesis (SyGuS) techniques. Our approach targets first-order theories without well-established quantifier instantiation techniques and higher-order quantifiers that can benefit from instantiations with \(\lambda \) -terms. By incorporating a SyGuS enumerator, our approach generates a broader set of candidate instantiations, including identity functions and terms containing uninterpreted symbols, thereby improving the effectiveness of MBQI.