In 1965 Dorman Long had plans drawn up for a new modern headquarters building designed by Sir James Stirling. The following photos of the plans and model were taken by Steve Collins in an exhibition at the Tate Modern in 2011, he’s kindly allowed me to use them, you can find his Flickr photostream here
Plans were advanced enough that a scale model of the proposed building was constructed.
Of course the building was never constructed because the company was nationalised in 1967 becoming part of British Steel. At first I had assumed it was to be built in the same location as the 1970s Steel House, but this photo montage suggests it was to be built further down the Trunk Road near Grangetown