I have searched both Google and this site. According to Collins, predispose can accept both to + infinitive and to + gerund. I find this questionable, but there it is.
Other than that, I can think of approach:
We need a new approach to win customers.
We need a new approach to winning customers.
Actually, in this case, it seems the infinitive works because of "need" and the gerund works because of "approach", so they're not actually saying the same thing.
I have seen on this site that prone does not work both ways, although people do use it both ways. It should only be used with to + gerund.
Are there other words or phrases that can accept to + infinitive and to + gerund equally?
*Note: I am not asking about "to" + infinitive vs. gerund. I am only asking about cases where the word "to" comes before the gerund, and also before the infinitive, and means the same thing. I have not found this question duplicated anywhere.
EDIT: And if the expressions do not always have the same meaning, can they ever have the same meaning?
EDIT: My current list, yea or nay?
well suited to do = well suited to doing
be adapted to do = be adapted to doing
proceed to do = proceed to doing
with a mind to do = with a mind to doing
agree to do = agree to doing
consent to do = consent to doing
donate to do = donate to doing