Mixing psints of different brands can be an iffy proposition. The general rule of thumb is to avoid mixing paints from different manufacturers if at all possible.
Generally speaking, mixing enamels of different brands may work successfully, Mixing Acrylics with enamels? No, usually you will end up with a ball of sticky goo.
Mixing acrylics of different brands also may or may not work. Not all acrylics are made equal. For example, mixing Tamiya and Gunze acrylics is usually ok, they are quite similar. Tamiya (or Gunze) mixed with Vallejo - probably not, (though I haven't tried) because they are quite dissimilar in formulation - their thinners are not cross-compatible.
Mixing a gloss and a flat to get a semi-gloss? This should work provided that the paints being mixed are from the same range (manufacturer) - One can also use a gloss or flat paint of the required colour and then overcoat with a semi-gloss clear finish - I'm not sure about other brands, but Humbrol makes a semi-gloss clear (lacquer?) finish.
I did read somewhere recently that someone was able to mix Tamiya acrylic (which had been thinned with lacquer thinner) with Gunze Mr Color (lacquer based), but this is something I'm not eager to try.
If the Model Master colour you wish to mix with the Tamiya colour is MM Acrylic, it may work, but if it's an enamel, I'd think it won't work. If the MM paint you wish to mix is indeed acrylic, test mix using a small quantity first. If you have lumps or strings that you can't stir out, I'd forget about it.