  Given two quasi-definite moment functionals, the corresponding orthogonal
polynomial systems satisfy an algebraic differential relation(called an
extended coherent pair). We study generalizing extended coherent pairs that
unify extended coherent pairs and extended symmetric coherent pairs and find
the related coefficients. When one of the moment functionals is (strongly)
classical, we find another orthogonal polynomial system to find three-term
recurrence coefficients. Moreover, we determine the companion moment functional
as a rational modification of the classical one.
