  The coherent transfer of excitations between different locations of a quantum
many-body system is of primary importance in many research areas, from
transport properties in spintronics and atomtronics to quantum state transfer
in quantum information processing. We address the transfer of $n>1$ bosonic and
fermionic excitations between the edges of a one-dimensional chain modeled by a
quadratic hopping Hamiltonian, where the block edges, embodying the sender and
the receiver sites, are weakly coupled to the quantum wire. We find that
perturbatively perfect coherent transfer is attainable in the weak-coupling
limit, for both bosons and fermions, only for certain modular arithmetic
equivalence classes of the wire's length. Finally we apply our findings to the
transport of spins and the charging of a many-body quantum battery.
