Flexible multibody (MB) dynamics comprises computational methods for predicting long time histories of motion in systems of interconnected rigid and deformable components undergoing large rigid body motion. Applications include vehicles, robotics, machines, mechanisms, and biomechanics. A widely used approach for modeling flexible bodies is the Floating Frame of Reference Formulation (FFRF), where a body’s configuration is represented as the rigid motion of a reference frame superimposed with small local elastic deformations. This separation allows standard component mode synthesis techniques, such as the Hurty/Craig–Bampton method, to approximate deformations by selected vibration and constraint modes, reducing degrees of freedom and enabling near real-time simulation. Consequently, the FFRF has become a standard for flexible MB simulations and is implemented in, e.g., RecurDyn, Adams, Simcenter 3D, MotionSolve, and SIMPACK. Flexible MB codes follow a standardized workflow where geometric and finite element (FE) modeling is performed externally. The FE model generates the data required for the FFRF, exported as a modal neutral file (*.mnf in MSC.ADAMS terminology), containing “invariants”—constant matrices sized according to the retained modes. These invariants are computed from the FE mass and stiffness matrices, reference nodal coordinates, and reduction basis, enabling setup and solution of the MB model without direct access to the FE code. Traditionally, model reduction is performed for a fixed set of parameters, including geometry, material properties, and boundary conditions. However, reduced models are generally not robust with respect to parameter variations, in particular changes in boundary conditions. This limitation is critical for applications such as control and optimization, where system parameters may vary across configurations or even during a single simulation. This contribution addresses the problem of parametric model order reduction for flexible MB systems modelled via FFRF. Specific problem formulations arising from different parameter dependencies are identified, and issues related to the interaction between FFRF and parametric reduction techniques are discussed. Suitable parametric model order reduction strategies are reviewed in this context. It is further shown that time-dependent parameters, which induce time-varying bases, give rise to additional elastic and inertia generalized forces within FFRF.