This paper focuses on the HOFiD_bvp code, initially developed by Amodio and Settanni in MATLAB for solving second-order scalar boundary value problems in ordinary differential equations. The objective of this study is to present an enhanced version of the code that can tackle problems involving one or more unknown parameters by incorporating an equivalent number of equations. Furthermore, the upgraded code demonstrates improved capability in efficiently handling discontinuous source terms and solutions. Several numerical experiments are conducted to showcase these novel features.