Advanced tools used in model-based systems engineering (MBSE) frequently represent their models as graphs. In order to test those tools, the automated generation of well-formed (or intentionally malformed) graph models is necessitated which is often carried out by solver-based model generation techniques. In many model generation scenarios, one needs more refined control over the generated unit tests to focus on the more relevant models. Type scopes allow to precisely define the required number of newly generated elements, thus one can avoid the generation of unrealistic and highly symmetric models having only a single type of elements. In this paper, we propose a 3-valued scoped partial modeling formalism, which innovatively extends partial graph models with predicate abstraction and counter abstraction. As a result, well-formedness constraints and multiplicity requirements can be evaluated in an approximated way on incomplete (unfinished) models by using advanced graph query engines with numerical solvers (e.g., IP or LP solvers). Based on the refinement of 3-valued scoped partial models, we propose an efficient model generation algorithm that generates models that are both well-formed and satisfy the scope requirements. We show that the proposed approach scales significantly better than existing SAT-solver techniques or the original graph solver without multiplicity reasoning. We illustrate our approach in a complex design-space exploration case study of collaborating satellites introduced by researchers at NASA JPL.