The Heckscher-Ohlin Model is normally presented for the case of 2 countries, 2 factors of production and 2 traded goods, leading to statements that, subject to free trade and various other assumptions:
A country with a relative abundance of a factor will specialize in and export the good whose production makes relatively intensive use of that factor (the Heckscher-Ohlin Theorem).
The return to a factor will be equalized between the countries (the Factor Price Equalization or Heckscher-Ohlin-Samuelson Theorem).
Do these results generalize, subject to the same assumptions, to cases with more than 2 countries, factors or traded goods, and what are good sources that treat this topic? Of particular interest are cases with 3 factors: labour, man-made capital and natural capital.
I appreciate that the predictions of the Heckscher-Ohlin Model often differ from empirical findings (eg the Leontief Paradox), but this question is about the model itself.