The preparation of CAD geometries for meshing and analysis poses a significant challenge in engineering simulations due to its labor-intensive nature. Over the last 20 years, various methods have been proposed to bridge the gap between CAD and analysis by requesting CAD to produce volume represents (V-Rep) suitable for the analysis . However, these methods do not integrate with modern CAD software (which do not produce V-Reps) and have not found wide industrial applicability. Our study extends the capabilities of the NURBS Enhanced Finite Element Method (NEFEM), a CAD-friendly technique that offers distinct advantages. NEFEM combines boundary representation (B-Rep) from common CAD packages with volume representation (V-Rep) from established meshing tools, resulting in a super-parametric element formulation for direct analysis of the CAD geometry. Our research introduces high-order quadrilateral elements and presents a comparison with their finite element counterparts. Through established benchmarks, the study demonstrates geometric convergence and underscores a superior CAD interoperability of NEFEM that could not be achieved with other methods.