If you have an EAD, then all is allowed; the question/issue is whether such an activity could negatively impact your pending I-485 application - and it could.
I on EB1B queue working at a uni, and was planning to consult for a Canadian firm, and the scope of work is related to my research area. This is not much info, but at a first glance, does it seems like it would negatively impact? Also my PD recently became current (not sure how long it will take to get the green card).