Will they offer lower rates than Amerisave? I thought there was no room for improvement beyond them, but it would be interesting to know otherwise. I refinanc

Will they offer lower rates than Amerisave? I thought there was no room for improvement beyond them, but it would be interesting to know otherwise. I refinanced through them and I check them from time to time to see current rates. I own a two-family house, and it is convenient that their web-site has an option to take this into account (rates slightly higher).