Although research has previously been done on multilingual speech recognition, it has been found to be very difficult to improve over separately trained systems. The usual approach has been to use some kind of “universal phone set” that covers multiple languages. We report experiments on a different approach to multilingual speech recognition, in which the phone sets are entirely distinct but the model has parameters not tied to specific states that are shared across languages. We use a model called a “Subspace Gaussian Mixture Model” where states' distributions are Gaussian Mixture Models with a common structure, constrained to lie in a subspace of the total parameter space. The parameters that define this subspace can be shared across languages. We obtain substantial WER improvements with this approach, especially with very small amounts of in-language training data.