In two types of infinitival clauses in the VO-language Lithuanian (purpose infinitives and infinitives em-
bedded under motion verbs), the direct object exceptionally surfaces to the left of the verb and bears a non-canonical case value (dative and genitive, respectively). This exceptional object shift is not observed when the infinitive contains a lexical verb that assigns an inherent case to its object that is more oblique than the case associated with the respective infinitival type. Existing analyses (Franks and Lavine, 2006; Arkadiev, 2014) cannot explain this link between obliqueness level and obligatoriness vs. non-availability of object shift. We develop a new cyclic analysis of the phenomenon that incorporates the strengths of both previous approaches while avoiding their weaknesses. In this analysis, both the local verb and a higher C-head in the structure assign different case values to the object of the infinitive (multiple case assignment), with the subsequent linearization procedure at PF being sensitive to a case hierarchy, resulting in different outcomes depending on the specific case values the object happens to bear. In order to receive case from the higher head, the object undergoes repair-driven movement up to the edge of the infinitival vP (PIC-accessibility); however, the linearization procedure may render this displacement covert, depending on the particular case values of the object. We draw additional evidence for the cyclic approach from structures with stacked infinitives, which neither one of the previous analyses mentions.