The intersection of two infinite matroids

Conjecture: Let M and N be two matroids (possibly of infinite ranks) on the same set S. Then there exists a set I independent in both M and N, which c an be partitioned as I = H boolean OR K, where sp(M)(H) boolean OR sp(N)(K) = S. This conjecture is an extension of Edmonds' matroid intersection theo rem to the infinite case. We prove the conjecture when one of the matroids (say M) is the sum of countably many matroids of finite rank (the other mat roid being general). For the proof we have also to answer the following que stion: when does there exist a subset of S which is spanning for M and inde pendent in N?