The paper introduces a new adaptive multivariable control algorithm that is able to manage processes that may present saturations on the control signals. This is the case when the calculated control signals go beyond boundaries. In many situations, the system under control may turn unstable if these limits are not considered. The first part of the paper describes the model of the process. The model consists of a variable number of inputs, because a control signal reaching saturation can no longer be considered as a free input. Next, the new control law is presented. It is based on a pole assignment strategy able to treat processes with a different number of inputs and outputs. The problem of minimising output errors when saturated inputs are present is also considered. An algorithm to recover, when possible, the control signals that are lost due to saturation is proposed. Finally, an example showing the algorithm behaviour is presented.