  The electron spin of a nitrogen-vacancy center in diamond lends itself to the
control of proximal $^{13}$C nuclear spins via dynamical decoupling methods,
possibly combined with radio-frequency driving. Long-lived single-qubit states
and high-fidelity electron-nuclear gates required for the realization of a
multiqubit register have already been demonstrated. Towards the goal of a
scalable architecture, linking multiple such registers in a photonic network
represents an important step. Multiple pairs of remotely entangled qubits can
enable advanced algorithms or error correction protocols. We investigate how a
photonic architecture can be extended from the intrinsic nitrogen spin to
multiple $^{13}$C spins per node. Applying decoherence-protected gates
sequentially, we simulate the fidelity of creating multiple pairs of remotely
entangled qubits. Even though the currently achieved degree of control of
$^{13}$C spins might not be sufficient for large-scale devices, the two schemes
are compatible in principle. One requirement is the correction of unconditional
phases acquired by unaddressed nuclear spins during a decoupling sequence.
