You shall surely open your hand to him. (Devarim 14:1)
The story is told that in the time of the Vilna Gaon, there was a very wealthy man who gave a lot of tzedakah, and then he lost all his property and became poor. The Vilna Gaon said this happened to him because he gave away more than a fifth to tzedakah, and one may not donate more than a fifth.
However, this matter is subject to a machlokes. There are views, and situations, in which it would be permissible to donate more than a fifth of one’s income to tzedakah.
Because the Rambam writes clearly in his Commentary on the Mishnah, at the beginning of Maseches Peah, that one may give more than a fifth, as an act of piety (chassidus). This also seems to be implied by the wording of the Rambam in Mishneh To r a h:
A person never becomes poor from giving charity, and no bad thing or harm is caused by charity, as it is stated והיה מעשה הצדקה שלום – “And the act of charity shall be peace...”.
The term “never” (l’olam) implies even if one gives more than a fifth.
And the Shitah Mekubetzes wrote that there is a difference between giving more than the prescribed amount for support of Torah study, which is permitted, and giving it to the poor, which is not.
This can be explained based on a verse from Mishlei:
For he who finds me finds life.
This pasuk, about Torah, teaches us that giving for Torah is not just tzedakah, but is giving for the very life of the soul, so you can never overgive.
Furthermore, it is written in the Tanya that regarding someone who has sinned, the following applies:
All that a person has, he should give for the sake of his soul.
This implies that one can give more than a fifth in order to attain kapparah for one’s sins.
It is not clear what the Vilna Gaon would say about all this.
R. Yosef Liss told me that the Brisker Rov once had a doubt concerning a certain sum of money that was sent to him. He went to great lengths, writing abroad, to clarify whether the money was meant for the Rav himself to use, or if it was sent to him for the purpose of distributing to tzedakah. R. Yosef Liss asked him, “Why trouble so much about? If there is a safek, just give it to tzedakah.” The Brisker Rov answered that if the money was in truth his own, and he gave it to tzedakah, he would thereby go over the chomesh (one-fifth) limit.
It seems, based on this story from R. Yosef Liss, from whom I learned in Yeshivas Beis Hatalmud, that the Brisker Rov followed the opinion of the Vilna Gaon, and did not rely on the aforementioned views.