How to cover a grid with another grid

Question

In Tikz I would like to display multiple overlapping grids such that the last one covers the previous ones. This is the code and the wrong output I get, where you can see the intermediate line of all grids. The fill=white parameter seems to not work.

\begin{tikzpicture}
    \foreach \i in {0, 0.5, ..., 1.5}
        \draw[fill=white, xshift=\i cm, yshift=-\i cm] (0, 0) grid (4, 4);
\end{tikzpicture}

Answer 1

It seems that you like to get the following:

Above image is composed from square shapes. One way to do this is:

\documentclass[tikz, margin=3mm]{standalone}

\begin{document}
\begin{tikzpicture}
\foreach \k in {0, 0.5, 1, 1.5}
{
    \begin{scope}[shift={(\k cm,-\k cm)}]
    \foreach \i in {0, 1,...,4}
    {
        \foreach \j in {0,1,...,4}
            \node[draw, fill=white, minimum size=1 cm, outer sep=0pt]
                  at (\i, \j) {};
    }
    \end{scope}
}
\end{tikzpicture}
\end{document}

Addendum: Simpler is to draw grid in rectangles with white fill:

\documentclass[tikz, margin=3mm]{standalone}

\begin{document}
\begin{tikzpicture}
    \foreach \i in {0, 0.5, ..., 1.5}
{
\draw[fill=white, xshift=\i cm, yshift=-\i cm] (0, 0) rectangle (4, 4);
\draw[xshift=\i cm, yshift=-\i cm] (0, 0) grid (4, 4);
}
\end{tikzpicture}
\end{document}

Result is the same as before