What is the best way to show a submenu in a tile menu design like Windows?

Recently, I designed a tiles menu and it is responsive, which means it will support desktop, tablet/iPad, and mobile devices. But I notice it is very hard to have a submenu in it. Can anyone please provide me some ideas for the best way to show the submenu in a tiles menu like Windows 10?

Here is the layout; the top left tile is the logo.

I have tried a slide menu, but it doesn't provide me the best solution. Because if I clicked at the bottom left tile, it will be a bit weird when the slide menu slides in from the right edge. The second reason is, there is a big gap: the user has to move their mouse from left to right edge and select the options. Also, because of the big gap issue, it makes the button and the active submenu lose their connection.