  A new approach for solving stiff boundary value problems for systems of
ordinary differential equations is presented. Its idea essentially generalizes
and extends that from arXiv:1601.04272v8. The approach can be viewed as a
methodology framework that allows to enhance "stiffness resistance"
capabilities of pretty much all the known numerical methods for solving
two-point BVPs. The latter is demonstrated on the example of the {\it
trapezoidal scheme} with the corresponding C++ source code available at
\url{https://github.com/imathsoft/MathSoftDevelopment}. Results of numerical
experiments are provided to support the theoretical conclusions.
