Use a pattern in the second argument of `Collect`:


    Collect[ExpandAll @ eq, x^_. y^_.]
>     x^4 c[1] + x^2 y^2 (3 c[1] - 2 c[3]) - x^4 c[3] + x^2 y^3 c[3] -   
>     y^4 c[3] - x^5 c[4] - x y^4 c[4] - x^6 c[5] - x^5 c[6] -  
>     2 x^3 y c[6] + x^4 y (c[1] - c[3] - 2 c[7]) +   
>     x^3 y^2 (2 c[2] - 2 c[4] - c[8]) + x^5 c[8] +   
>     x^4 y^2 (c[5] - c[9]) + x^6 c[9] + x^6 y (-c[5] + c[9]) +   
>     x^5 y^2 (-c[4] + c[10]) + x^5 y (-2 c[4] + 2 c[10])