Handling mobility at the transport layer is a promising approach to achieve seamless handover in the context of heterogeneous wireless access networks. In particular, features such as multihoming and dynamic address reconfiguration provided by mobile SCTP (mSCTP) protocol are among the key enablers for handover support at the transport layer. This paper investigates the applicability of Concurrent Multipath Transfer (CMT) to distribute data among two end-to-end paths of a mSCTP association during handover transition process. To that end, the principles of the mSCTP-CMT design are given, emphasizing the consequences of such a sender-introduced reordering and its congestion control implications in a handover scenario. The proposed mSCTP-CMT handover scheme is benchmarked with a pure mSCTP handover scheme. Provided analysis indicates the possible application area of mSCTP-CMT, taking into account not only handover scenario parameters (dwelling time, available bandwidth ratio and round-trip time), but also the most important constraint of such a design: receiver buffer (rbuf) size. Rbuf size proves to be the major limiting factor shrinking significantly possible mSCTP-CMT application scope, yet not excluding definitively the proposed idea.