Generalization of the Heckscher-Ohlin Model 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.
The HO model has been generalised. Vanek does a good job of it. 

Instead of only two countries, there is an index of countries.


There are many industries.
Identical technology
Identical, homothetic tastes.


The HOV theorem states that if a country is abundant in a factor,
its factor content of trade in that factor should be positive, and
negative otherwise.

Empirically, this model is not that successful. Here is a good paper discussing the applications and results.

See below for that extension:
Vanek, Jaroslav, The Factor Proportions Theory: The N-Factor Case,” Kyklos, October 1968, 21, 749-755.