Looking at Rail Map Online and swapping current and old map bases, it appears that the "footprint" of the current station includes almost all of that of the previous one. This is confirmed by the cutting walls in all four corners of the station being brick which is obviously older than the concrete of the station itself. The exception is an area on the south side that might have made a few shortish bay platforms but no through platforms (the tracks each end would have been at almost 90 degrees to each other) but would have made the throats evan more complicated than they are today. New Street also took over the small road that ran between the LNWR and Midland side. The plan linked below shows that prior to the 1960s rebuilding, New Street had eight through platforms and six bays, plus three short sidings in the southern area mentioned. The current station has 12 through platforms (each of which can take two short trains) and one bay.
http://www.warwickshirerailways.com/lms/lnwrbns_str1310.htm
So I think the 1960s station made a pretty good job of providing the maximum platforms in the available land, and resulted in considerable increase of capacity over what preceded it.
I agree that increasing the footprint would not have been considered either then or now, as due to the curvature on the south side this would have involved taking a slice of the main shopping area to the north.
By contrast Snow Hill had eight through platforms at its maximum (four long platform faces, each with different numbers either end of crossovers to through tracks) and four bays. Closing this station resulted in a net reduction of platform capacity in central Birmingham despite the extra platforms at New Street. The current Snow Hill has only three through platforms, with the possibility of a fourth being restored when the Midland Metro moves out.
) and then go down (if you can find a working escalator) close to the time your train is due in.
