Based on sate, new words formed by adding one letter at the beginning or end:
b - aest c - abets d - baste e - beast f - beats g - betas h - tabes j - caste k - cates l - cesta m - taces n - sated o - stade p - stead r - tsade s - setae t - fates u - feast v - feats w - fetas x - gates y - getas z - stage