Years ago I managed a sales team for a payroll service company. 50% of our business came from CPA referrals because we called on the accounting community, developed strong relationships with them and then continued those business friendships.
So this is a little different than asking everyone for three referrals. Cathy asked the same person for referrals three TIMES over a period of several weeks or longer. They got to know her and felt comfortable by the third time she asked to them to deliver the valued name.
Does your type of sale offer the opportunity to see a prospect multiple times, enabling you to allow the to get to know you fairly well?