We investigate the complexities of clitic agreement patterns in Phorhépecha (language isolate, Michoacán). We show that clitics in the language display a preference for agreeing with participant objects in monotransitive sentences: whenever the object is a participant, regardless of the person features of the subject, clitics invariably agree with the object and not the subject. Further, we demonstrate that clitics exhibit omnivorous number agreement (Nevins 2011). A single morphological marker of plurality on clitics surfaces when two conditions hold: (1) whenever a subject, object, or both are plural, and (2) if the object is a participant. If the object is third person, clitics do not display omnivorous number agreement, and instead agree solely with the subject. We argue that these complex and interrelated patterns of agreement are due to relatively simple syntactic mechanisms. Firstly, we submit that clitics themselves are functional heads (following Sportiche 1996) that probe for person and number. Secondly, we propose that participant objects undergo object shift to a position above subjects and closer to the person probe on clitics, which, we maintain, captures the preference of clitics to agree with participant objects. Thirdly, we attribute omnivorous number agreement to a relativized number probe on clitics, which searches for any plural argument (subjects and objects) within the probe's c-command domain. Finally, we adduce independent evidence for our movement-based analysis from verbal agreement. In Phorhépecha, verbs agree with plural objects only if those objects are third person. We claim that verbal object agreement arises with third-person objects, and not participant objects, because only the former do not undergo object shift and instead remain in their base positions, from which they are accessible to a number probe within the extended projection of the verb. In contrast, participant objects shift to a higher position and are consequently inaccessible to said number probe.