This paper shows that the accuracy in T-spline based isogeometric analysis may be substantially improved by increasing the multiplicity of the inner knots up to the polynomial degree. This task can be performed considering the Bézier extraction operator matrix elementwise, and thus easily receiving an increased number of updated control points in the geometrical and computational model. Nevertheless, after the determination of the unique control points, sometimes the Bézier elements near the T-junctions may not be well-shaped, and thus minor automatic interventions are required to ensure full (i.e., C0 and G0) compatibility. The improved IGA solution may be also used as a reference to determine the a-posteriori error estimations in the T-spline elements of the domain. The methodology is shown in BVPs dominated by Laplace-Poisson equations in rectangular and curvilinear domains, while eigenvalues were extracted in a rectangular acoustic cavity.