Power linear Keller maps with ditto triangularizations

We show that power linear Keller maps F=(x1+(A1x)d,x2+(A2x)d,…,xn+(Anx)d) are linearly triangularizable if (1) rkA 2 or (2) corkA 2 and d 3 or (3) corkA=3, d 5 and the diagonal of A is nonzero. Furthermore, we show that the triangularizations can be chosen power linear as well.