  For $r\in \Z_{\geq 0}$, we present a linear differential operator
%$(\di)^{r+1}+ a_1(x)(\di)^{r}+...+a_{r+1}(x)$ of order $r+1$ with rational
coefficients and depending on parameters. This operator annihilates the
$r$-multiple Jacobi-Pi\~neiro polynomial. For integer values of parameters
satisfying suitable inequalities, it is the unique Fuchsian operator with
kernel consisting of polynomials only and having three singular points at $x=0,
1, \infty$ with arbitrary non-negative integer exponents $0, m_1+1, >...,
m_1+...+m_r+r$ at $x=0$, special exponents $0, k+1, k+2,..., k+r$ at $x=1$ and
arbitrary exponents at $x=\infty$.
