I can point to any number of examples to show how it could be a fraction of the cost (and have done several times).
We really don't have to look too far for an obvious one (a few hundred metres across the park), which was only approx £200m construction cost to get from 45k to almost 62k capacity (it would've been less if they'd done both at the same time). I stood in the upper tier of another on Tuesday night, that cost far less again to go from 36k to 52k. There ard many more besides. So it's hardly a great mystery.
The simple maths is, it is almost always far cheeper to add say 20k or 30k capacity to an existing stadium, than to build a whole new 50k+ stadium from scratch. Which is why the majority of larger clubs have chosen the former approach. That theory even applies to the mega-rich clubs like Real Madrid and Barcelona who have both chosen redevelopment over new-build..... to prove that they need not be cheap and nasty addlibs. Obviously, for smaller clubs, the sale of their existing site would often cover the bulk or even all the costs of a new build. That rarely applies to those seeking stadia over 35k, since cost per seat rises almost exponentially with capacity.
Depending on the format chosen, 27k (or as high as 35k) of GP is entirely recyclable capacity. If 1, 2 or even 3 of the existing upper tiers were replaced with whole new tiers, and Park end expanded too to reach BMDs capacity... Then, even at Anfield's cost per seat for construction, it would only be £150-270m. The actual cost per seat would be less, because the starting construction height would be considerably lower on both the Gwladys St and Bullens Rd stands, because both lower tiers are much lower than those built over at Anfield. Therefore, there would be significantly less construction volume in total too, which is the greatest cost determining factor. So you could probably trim those figures by 30%+.
You could also extrapolate those numbers further to reach 60k or 65k capacity at GP. So, whichever way you want to cook it, the cost is a fraction of BMD everytime, because building 20-35k new capacity is always cheaper than building 53k... even more so when it costs £150m just to prep the new site, and conserve the surroundings.