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You could, but I wouldn't recommend it.

Learning a new language, say C++ -> Java is WAY more than just learning the syntax. There are best practices for solving certain kinds of problems in each language that differ between language.

Sure, there is a high level similarity between the solutions (hey, its just the observer pattern, right?), but there are also likely (IME) to be many critical differences in the details.

You could probably write C++ code in C#, Java and PHP, but it would be hideous. I've seen Fortran written in C, and Pascal written in C++, and C written in Java, and it's generally an unholy mess.

That may be true for many languages, but if those people never roll into that sort of situation it's probably fair to still call them programmers.