Well, my comment has gotten too big, so I'll leave it here.
Yes, it is possible. But start with mobile , then bigger screens up to desktop (which already exists in your case, apparently). Define the layout you want and pay attention to the settings range ( 320 × 240 up to 640 × 960 ).
Use media queries appropriately. I will not write any here, but know that CSS Tricks (more than recommended) already has all the most commonly used snippets .
!!! Pay attention!
Some elements of your site will simply not exist in the mobile version, you have to remove them, either for lack of space or for another factor, and that is okay !
1.1 Think about how the menu will be shown. See this example of CSS Tricks
The mobile version is always the one that offers a push of a button, nothing else (figurative), does not let the client think in> Eg: If the site features are in an area that needs login , show login right away, you do not need to show the slider >, for example.
Search for plugins to make your service easier. There are many like Isotope
Tip : Type the CSS for each type of screen you want to support in separate .CSS files, this will help with maintenance.