Embodiments of an orthopedic implant device and system, and methods for implanting them, are disclosed. The implant may include a receiver member having a channel for accommodating an elongated rod or other longitudinal member, a bone anchoring member such as a screw or hook, and a base member rotatable with respect to the receiver member for retaining the bone anchoring member in the receiver member. The base member is configured to allow at least two different degrees of maximum angulation of the bone anchoring member with respect to the receiver member. The number and relative direction of such angulations are independent of the orientation of the channel or other part of the receiving member.