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Beam splittings with an arbitrary number of beams of in- and output are introduced as second quantisations of isometric operators of matrix-multiplication. They are also characterised as the only vacuum-preserving isometries on multiple symmetric (bosonic) Fock space which are factorisable (tensor-decomposable) by regions. Studying this kind of operators was part of a close collaboration with neuroscientists to develop a quantum model of the recognition of signals in the brain. Definition and characterisation of beam splittings mentioned above show, that the interaction of signals coming from the senses and those generated by the brain (representing an expected view of the world) is meaningfully modelled by such a beam splitting operator. Thereby, regional factorisation of the operator of interaction corresponds to a parallel processing of partial signals belonging to different regions of the brain.