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Recent proposals for reconfigurable data center networks have shown that providing multiple time-varying paths can improve network capacity and lower physical latency. However, existing TCP variants are ill-suited to utilize available capacity because their congestion control cannot react quickly enough to drastic variations in bandwidth and latency. We present Time-division TCP (TDTCP), a new TCP variant designed for reconfigurable data center networks. TDTCP recognizes that communication in these fabrics happens over a set of paths, each having its own physical characteristics and cross traffic. TDTCP multiplexes each connection across multiple independent congestion states---one for each distinct path---while managing connection-wide tasks in a shared fashion. It leverages network support to receive timely notification of path changes and promptly matches its local view to the current path. We implement TDTCP in the Linux kernel. Results on an emulated network show that TDTCP improves throughput over both traditional TCP variants, such as DCTCP and CUBIC, and multipath TCP by 24--41% without requiring significant in-network buffering to hide path variations.