No such thing as too many Hadassim!
In Parashat Emor, the Torah commands:
“And you shall take for yourselves on the first day the fruit of the hadar tree, branches of palm trees, and the boughs of thick leaved trees, and willows of the brook; and you shall rejoice before the Lord your God seven days.” (Vayikra 23:40)
Whilst it is clear that all four species are required, the Torah is not explicit regarding how many of each species need be used.
Our Rabbis explain that one lulav is all that is needed (Sukkah 34b), and as suggested in the passuk, one esrog is used. The generally accepted halacha follows the opinion of Rabbi Yishmael in that Gemara, who says that three hadassim and two aravos are used (Rambam, Tur & Shulchan Aruch, Orach Chaim 651:1). However, as hadassim and aravos are mentioned in plural form, it is implied that there is no limit and one may as many branches of these species as they like.
The custom of adding hadassim may actually go far back into Jewish history, as coins from the Bar Kochba era have been found that indicate the use of many hadassim.
The coin above is a Silver Sela dated to 132-135 CE and says 'Year one of the redemption of Israel' in Paleo-Hebrew. This may be a reference to the opinion of Rabbi Akiva that Bar Kokhba was Mashiach. The image depicts a lulav bound with many hadassim and only two aravos. It is worth noting that the esrog depicted has a “garter” or belt, as is preferred by some present day minhagim.
Indeed, the Yemenite custom is to add many hadassim, even branches which that do not necessarily have triple leaves. Rabbi Saadiah Gaon in his siddur writes that "one may add to the two aravos and three hadassim with as many hadassim as one wishes that are not three-foil [“meshulashim”], until the bundle is filled out." Yemenite practice in this regard was also ruled on by Rabbi Yihye Zalah (Mahariz), one of the greatest Yemenite poskim, who lived in the 18th century (Takhlal Etz Hayyim, S. Zalah ed., 2, p. 334)
Likewise, the Chabad custom is to add at the very least an extra three hadassim, besides the standard three required by halacha (13th Tishrei 5752; Sichos Kodesh p.98). The Otzer Minhagei Chabad quotes the Rambam Hilchot Lulav (7:7) stating that this is a “נוי מצוה”.
The Lubavitcher Rebbe suggested that chassidim should use at least six hadassim. However, there were times when the Rebbe himself would use a lulav with 18 hadassim, corresponding to the word “Chai - Life” There were also times when the Rebbe used 26 hadassim, corresponding to the numeric value of G-d’s name, the Tetragrammaton. Some years, the Rebbe even used 36 hadassim, corresponding to double “Chai”.
It is worth noting that some poskim also reference customs of using 68 hadassim corresponding to the numeric value of the Hebrew word “lulav”, whilst others mention a custom of using 100 hadassim!