We present new data from ongoing work on a variety of Maithili (Indo-Aryan, Nepal), with striking implications for theories of phase impenetrability, minimal search, and anti-agreement. We find a number of patterns overlooked in previous work on this variety (Yadava et al. 2019, Alam and Kumaran 2022). Notably: 1. in some cases, a verb agrees with the possessor of an argument without the possessor undergoing focus movement to the argument's edge (suggesting that arguments are not impenetrable phases); 2. the object seems to have priority over the possessor of the subject for agreement (posing a challenge for minimal search—why should the object count as closer to the probe than the subject's possessor?); 3. focused non-subjects can condition mismatched / default subject agreement (which can be thought of as a special case of anti-agreement, building on Baier 2018).