Is "Next to that" really an alternative to "Additionally" or "Moreover"?
Solution 1:
Your instincts are correct: "next to that" is not something a native speaker would use if they wanted to say "additionally". Given enough context, most native speakers would understand what was meant, mind you, but like Robusto said, it's an odd, foreign-sounding locution. (Also, it might be misinterpreted as an attempt to say "besides".)
The phrase can be used literally, i.e. when talking about physical proximity, or it can be used with a sense of comparison, as in Jay's "Next to that, the $1 million ... is a minor problem". But just like none of those usages would work if you substituted "additionally", you can't really use "next to that" when you mean "furthermore".
Solution 2:
It's not wrong in English. You might say, for example, "Bob owns a car and a motorcycle. Next to that he also owns a boat."
In a similar way we also say "in addition to that" and "besides that".
"Next to that" can also be used literally, to mean that something is physically adjacent. Like, "On the desk is a pencil. Next to that is a pen." The pen is adjacent to the pencil.
"Next to that" is also used to make comparisons. Like, "The company lost $10 million on the failed product roll out. Next to that, the $1 million that we lost when the factory burned down is a minor problem."