Overcoming Eager Evidence

Does anyone know any good way to make a point that one believes is true on its own merits but clearly benefits the speaker or is easier for the speaker?

Suppose a poor person is saying we should all give more money to poor people, are there ways to mitigate the effect of “You're only saying that to benefit yourself” beyond either finding someone else without that perceived (and likely actual, but maybe less than perceived) bias or just taking the hit and having a strong enough case to overwhelm that factor?