See Mishnah Berurah 651:59
דכתיב ולקחתם לכם ביום הראשון פרי עץ וגו' משמע אחד ולא שנים וה"ה ללולב דכתיב כפות תמרים חסר וי"ו דהיינו אחד וי"א דעובר בזה גם על בל תוסיף אבל בערבה לא נתן בה תורה קצבה והאי דקי"ל דבעינן שתי ערבות משום דכתיב ערבי נחל היינו דבהכי סגי דמיעוט ערבי שתים אבל טפי ג"כ שפיר דמי וה"ה בהדס דכתיב ענף עץ עבות ג"כ יכול להוסיף כמה שירצה
In short: we have pesukim which imply only one lulav and esrog, but no such pesukim exist for hadassim and aravos.
I found two instances of the Minhag to add extra hadassim and/or aravos (above the standard 3):
As a Chabad minhag over here:
It is the Chabad custom to add at the very least an extra three myrtles (Hadasim), besides the standard three required by Halachah. (13th Tishrei 5752; Sichos Kodesh p.98)
And as a Yemenite practice over here:
The Yemenites use more than two branches of willow and three of myrtle, adding branches of myrtle that do not necessarily have triple leaves. This is mentioned by Saadiah Gaon in his prayer book (pp. 236-237): "One may add to the two branches of willow and three stems of myrtle as many as myrtle branches as one wishes that are not three-foil [meshulashim], until the bundle is filled out." Yemenite practice in this regard was ruled on by Rabbi Yihye Zalah (Mahariz), the greatest Yemenite posek, who lived in the 18th century (Takhlal Etz Hayyim, S. Zalah ed., 2, p. 334):
In this same source of Yemenite practice I found a reasoning defending that it's not Bal Tosif:
since it is a variety of myrtle [and not the addition of a fifth type to the four species], as written in Sefer Tanya by the geonim.