I am adding a whole new section to a website using Twitter Bootstrap 3, however the container cannot go wider than 940px in total for Desktop - as it will throw out the Head
The best option is to use the original LESS version of bootstrap (get it from github).
Open variables.less and look for // Media queries breakpoints
Find this code and change the breakpoint value:
// Large screen / wide desktop
@screen-lg: 1200px; // change this
@screen-lg-desktop: @screen-lg;
Change it to 9999px for example, and this will prevent the breakpoint to be reached, so your site will always load the previous media query which has 940px container