株立
kabudachi are the characters making this bonsai word. Kabu is the word for stump (but is also used for stock i.e. stock market etc) and Dachi which is to stand or rise. It would be considered an informal tree style in Japanese bonsai circles. This is different from the Soukan or Sankan; Split Trunk, with two main trees or Three Tree split at the trunk base respectively. So technically what you will have with this Hornbeam is a Sankan, which is considered an informal style. Soukan style interestingly is considered a semi-formal style. The reason Japanese do not do four trunks is because in Japanese the word Four is considered unlucky, sometimes pronounced yon and sometimes pronounced shi. Shi is the word for death, and so it is an unlucky number, just like some Americans consider 13 to be an unlucky number. So most Kabudachi styled trees are going to limit the trunks to five.....more than that number and it would probably look unwieldy or like it was pollarded to death? Here is reference to a resource on the site.
Gaddou Display Basics
To ad to kekejiku's detailed response.
Based on what I've seen, "Kabudachi" is a minimum of 5 trunks, only because the categories of 双幹 "soukan" (pair of trunks), and 三幹 "sankan" (three trunks) exist. That's not to say, soukan and sankan cannot also be kabudachi. They absolutely can. If there are 2 or more trunks that are fused and share a nebari, then I think you are free to call it kabudachi although most would likely just identify it by the number of trunks instead. It's like saying all apples are fruits, but not all fruits are apples.
As far as maximums go, there isn't one as far as I know. However, it depends how the tree was built/grew. If it was technically a raft (an original trunk layed down, with the branches forming new trunks), then it becomes 筏吹き "Ikadabuki". However, unless one knew the history of the tree, it's likely they might look at a raft and say, "That's a nice kabudachi.", and have the owner reply, "That one is actually and ikadabuki."
Also, to add to the number 4 thing: It's true to the point that some older buildings don't have a 4th floor. To a lesser extent, the number 9 has some stigma as well because one of the ways the number 9 can be pronounced resembles the pronunciation for words that involve pain or suffering.
I got into my last apartment because it was on the 4th floow and nobody wanted it. - It did however turn out to be unlucky as my neighbor there had an extreme case of OCD and was insufferable to live next to.
Now I live on the 7th floor of another building. : )