AEW Architects has been ordered by the High Court to pay a further £1.24m damages to National Museums Liverpool in addition to £1.1m awarded last month.
The High Court decision relates to design faults on ceilings, including one which is understood to have partially fallen in, as well as the cost of replacing faulty structures and of storing artefacts whilst repairs were carried out. The initial award in July was for external steps and terraces.
Sharon Granville, director of the Museum of Liverpool, said she was "very pleased with this latest settlement".
Interest and costs are due to be awarded in October.
Steve Burne, managing director of AEW, based in Manchester, said: "This is the final stage relating to the judgement, which was first issued on 31 July and we are glad that this matter is now concluded."
Burne said the amount of damages was less than the initial claim and £205,000 was being paid by contractor Galliford Try Pihl.
National Museums Liverpool replaced 3XN with AEW in 2007.