PORTSMOUTH, N.H. – Hillary Clinton said Saturday that she is open to taking part in more primary debates than the half dozen sanctioned by the Democratic Party, ramping up pressure on party leaders to bulk up a debate schedule that some candidates say is too thin.

As it now stands, the Democratic National Committee has scheduled six debates, four of which come before the Iowa caucuses on Feb. 1. Democratic Party leaders have also taken the unusual step of imposing an “exclusivity” provision punishing candidates who take part...