Hi Saif,
You can create separate CSS files (for example ClientID+suffix.css) for each client and in OnReady event of your Layout you can load the CSS dynamically using javascript code some thing like below
var link = document.createElement( "link" );
link.href = file.substr( 0, file.lastIndexOf( "." ) ) + ".css";
link.type = "text/css";
link.rel = "stylesheet";
link.media = "screen,print";
document.getElementsByTagName( "head" )[0].appendChild( link );
Best Regards
Devendra