Good question!
This depends on how liquid are you. Hopefully not more than 3 months salary, as there are opportunities elsewhere.
If it is less than 3 months salary, best to keep it liquid as possible, and the amount wouldn't be able to be leveraged for large sums from marginal gains. So follow on if it is more than 3 months salary, and only use the excess of the 3 months salary.
What we are assuming though are two parts: inflation will wipe out some of the value, which you want to hold, and there are opportunity costs to keeping money purely liquid.
Based on that, yes invest the excess elsewhere. As to focusing on other currencies than the US dollar, there is another thought to this. Why focus on foreign currencies as the only investment instrument? If it is a concern of keeping everything quite liquid still, then yes, go for another currency. If it is looking for an investment opportunity, then please look at other investment instruments (stocks, bonds, futures, etc).
Best of luck