This paper presents a model reference adaptive control scheme for deterministic continuous-time multivariable systems represented by square, strictly proper, minimum-phase transfer function matrices. A typical requirement of existing algorithms is to assume that the zero structure at infinity and the high-frequency gain matrix are fully (or at least partially) known. It is well known that these requirements may be very restrictive, since in general both the zero structure at infinity and the high-frequency gain matrix depend on plant parameters. In this paper we show that these restrictive assumptions may be considerably weakened using a hysteresis switching control strategy recently introduced by Morse et~al. The strategy entails running a finite number of parameter estimators in parallel, and using a switching algorithm to select between candidate estimators based on their associated prediction errors. Hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators, and all switching ceases within a finite time. The results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system.