  This paper delves into classical multiple orthogonal polynomials with an
arbitrary number of weights, including Jacobi-Pi\~neiro, Laguerre of both first
and second kinds, as well as multiple orthogonal Hermite polynomials. Novel
explicit expressions for nearest-neighbor recurrence coefficients, as well as
the step line case, are provided for all these polynomial families.
Furthermore, new explicit expressions for type I multiple orthogonal
polynomials are derived for Laguerre of the second kind and also for multiple
Hermite polynomials.
