  For a smooth projective curve, the cycles of subordinate or, more generally,
secant divisors to a given linear series are among some of the most studied
objects in classical enumerative geometry. We consider the intersection of two
such cycles corresponding to secant divisors of two different linear series on
the same curve and investigate the validity of the enumerative formulas
counting the number of divisors in the intersection. We study some interesting
cases, with unexpected transversality properties, and establish a general
method to verify when this intersection is empty.
