Victoria Thornley in the women's single sculls and Katherine Copeland and Emily Craig in the lightweight women's double sculls were among those who qualified.
Earlier on Saturday in Poland, Lauren Rowles and Laurence Whiteley won silver in the PR2 mixed double sculls.
Joel Cassells and Sam Scrimgeour also won silver in the lightweight men's pair.
That event was won by Irish pair Mark O'Donovan and Shane O'Driscoll, with Brazil taking the bronze.
Sunday's action sees Britain also compete in finals across the men's four, men's quadruple sculls, women's pair, the women's eight, the men's eight and the men's single sculls.
Live coverage begins on the BBC Red Button from 09:25 BST.
Britain will have eight boats competing in medal races on Sunday's final day of racing at the World Cup II in Poznan.