Asian American are finding a pan-ethnic identity, but only to a limited extent. There are forces that pull Asian Americans together, but there are also forces that pull them apart into separate ethnicities.
Asian Americans are pulled together mostly by census definitions. Since we (I am Asian American myself) are placed together in one category, we often end up interacting on that basis. We have things like Asian American clubs at colleges. These pull us together.
At the same time, however, there is a great deal that pulls us apart. to take but one example, Japanese Americans are separated from other Asian Americans by history. The history of Japanese conquest and occupation of other Asian countries like Korea and the Philippines in WWII makes it very difficult for Americans of Korean and Filipino descent to feel an affinity with Japanese Americans.
Thus, there are forces that are creating something of a pan-ethnic identity. However, this identity is by no means very strong nor is it universally felt.