Towards extending the Ahlswede-Khachatrian theorem to cross t-intersecting families

In a previous paper we showed a cross t-intersecting version of this for large t in the case that r=0. In this paper, we do the same in the case that r=1. We show that for p in the range [1t+1,2t+3] the maximum p-weight of a cross t-intersecting pair of families, for t≥200, is achieved when both families are F1t. Further, we show that except at the endpoints of this range, this is, up to isomorphism, the only pair of t-intersecting families achieving this weight.