Efficient techniques exist for the design of supervisors enforcing constraints consisting of linear marking inequalities. This note shows that without losing the benefits of the prior techniques, the class of constraints can be generalized to linear constraints containing marking terms, firing vector terms, and Parikh vector terms. We show that this extended class of constraints is more expressive. Furthermore, we show that the extended constraints can describe any supervisor consisting of control places arbitrarily connected to the transitions of a plant Petri net (PN). The supervisor design procedure we propose is as follows. For PNs without uncontrollable and unobservable transitions, a direct method for the design of a PN supervisor that is least restrictive is given. For PNs with uncontrollable and/or unobservable transitions, we reduce the problem to the design of supervisors enforcing linear marking inequalities.