This paper examines a pattern of number agreement in the four Kartvelian languages (Georgian, Laz, Megrelian, Svan), in which the spell-out of a lower agreement probe affects agreement on a higher agreement probe. Specifically, the higher probe shows plural agreement if the lower probe does not lexicalize a plural feature, and does not show plural agreement if the lower probe lexicalizes a plural feature. Departing from morphological accounts of Kartvelian number agreement present in the literature (Halle & Marantz 1993, Lomashvili & Harley 2011, Blix 2020, a.o.), the authors argue that this interaction between the two probes is syntactic in nature and arises due to what they call Leftover Agreement -- agreement by a higher probe with the unlexicalized features of a lower probe. The authors argue that their account provides evidence for a certain kind of interleaving of syntax and spell-out, and motivates an architecture in which Vocabulary Insertion is only partially replacive: exponents replace only those features that their specification matches exactly.