  In arXiv:1710.01672, we obtained general type results for orthogonal modular
varieties associated with moduli spaces of compact hyperk\"ahler manifolds of
deformation generalised Kummer type (also known as 'deformation generalised
Kummer varieties'). The orthogonal modular varieties were defined in terms of
an integer 2d, corresponding to the degree of polarisation of the associated
hyperk\"ahler manifolds. In arXiv:1710.01672, we showed these orthogonal
modular varieties are of general type when 2d is square-free and sufficiently
large. Here we show that the square-free condition can be removed.
