Finding a \emph{maximum} cardinality common independent set in two matroids (also known as \textsc{Matroid Intersection}) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum bipartite matching, a maximum colorful forest, and an arborescence in directed graphs. Enumerating all \emph{maximal} common independent sets in two (or more) matroids is a classical enumeration problem. In this paper, we address an ``intersection'' of these problems: Given two matroids and a threshold $\tau$, the goal is to enumerate all maximal common independent sets in the matroids with cardinality at least $\tau$. We show that this problem can be solved in polynomial delay and polynomial space. We also discuss how to enumerate all maximal common independent sets of two matroids in non-decreasing order of their cardinalities.