In applications, it is usually desirable to implement the simplest controller in terms of signal interconnections and controller order. In accordance with this goal, this paper presents an adaptive output-feedback control technique for MIMO systems, where the order and structure of each SISO entry of the controller can be assigned an arbitrary parameterization. The first parameterization is based on a MIMO input-output model of fixed window length. The second parameterization constrains all SISO entries of each row of the controller to have the same denominator of specified order; the third parameterization constrains all SISO entries of the controller to have the same denominator of specified order; and the fourth parameterization allows complete flexibility in setting the structure and order of each SISO entry of the controller. PID, infinite impulse-response, finite impulse-response, and sparsely parameterized controllers can be specified as special cases. This paper 1) defines the regressor structure for each parameterization; 2) enumerates the number of updated coefficients of each parameterization; 3) provides bounds on the McMillan degree of each parameterization; and 4) provides numerical examples to illustrate the relative effectiveness of each parameterization.