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The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of 3 and 4 interacting qubits.