As far as I'm aware, the historical practice of Ashkenazim was to have only one person recite each Kaddish. This is derived from the Gemara in Megillah (~21b) where it is said that תרי קלי לא משתמעי, "two voices are not heard [together]." This also fits with a midrashic statement that saying יהא שמה is a comfort to the neshamah of the deceased (citation needed).
While German-influenced kehillot still often oppose the group Kaddish, it has become fairly common in most circles. In some non-Orthodox communities, everyone will say each Kaddish together, so that there is no one to say אמן or יהא שמה!
What sources are provided for the practice of group Kaddishin among Ashkenazim, especially with regards to תרי קלי and saying/responding יהא שמה?