Minimal realizations are a key feature in systems theory/applications. In the case of nD linear systems (i.e. systems where transfer function descriptions are functions of n > 1 indeterminates), however, the problem of the existence and construction of such a realization is still an open problem with solutions available in only a few special cases. This paper adds one more case to this list in the form of a single-input single-output linear system where denominator and denominator polynomials of the transfer function description are multi-linear polynomials, i.e. they are of degree one in each indeterminate. Also in the case when an absolutely minimum realization does not exist, the use of the elementary operations algorithm (EOA) to produce non-minimal realizations with a moderate degree of redundancy (or even of least order) is advocated.