R'uvein and Gad approached Moshe Rabbeinu requesting TransJordan. When Moshe acquiesced, he added Hatzi Shevet M'nasheh. Why?
Below is a an answer based upon the structure of the Tribes throughout Sefer Bamidbar - here is that dynamic at work
When Levi drops out of the "tribes" a shuffle occurs in Parshas Bamidbar, Nasso, B'haalot'cha. *
1. Gad is promoted to Honorary Ben Leah, camping with R'uvein and Shim'on
2. Yosef is divided into Two, Ephraim and M'nasheh to restore the number to 12
The 4 camps now are structured as follows
East - 3 from Leah
South - 2 from Leah plus Gad
West - 3 from Rachel
North - 3 from the "sh'fachot" - 1 from Zilpah, 2 from Bilhah
Levi was now in a circle inside
When R'uvein and Gad chose TransJordan, then we have
20% of Leah
25% of the Sh'fachot
0% of Rachel
To Remedy this Moshe takes 1/2 of M'nasheh which comprises about 25% of Rachel - thereby restoring a balance of Imahot. [Counting Bilhah/Zilpah as a unit]
Why M'nasheh and not Ephraim? I'm not sure - but perhaps it is since he is the b'chor and so are R'uvein and Gad.
* Note whenever Levi IS counted in the 12, Joseph is reunited.