In some countries, this is how many people learn foreign languages at school. This was the case when I was attending school in Belgium in the 1980s and early 1990s: we started with French in the fifth year of primary school, I added Latin in secondary school, English in the third year of secondary school, and German one year later. There are other countries where learning two or more foreign languages in parallel is not unusual.
However, what you do in your spare time is a different matter. In that case, your decision to add another language depends mainly on two things: time and motivation.
The time aspect was already mentioned in the question. In theory, adding another language would double the time you need to achieve mastery. However, if your native language is a Germanic language, you may find that Japanese requires roughly three times the amount of effort than German. This ratio does not improve much (if at all) if your native language is a non-Germanic Indo-European language. You'll need to manage your time so you spend at least 30 minutes on Japanese every day. (When I was attending Spanish and Chinese language courses in parallel for some time, I spent at least 30 minutes per day on Chinese and 60 minutes per week on Spanish.)
The other aspect is motivation. Knowing why you want to learn the language will enable you to set specific goals and will keep you motivated. On the Mezzofanti Guild website, Donovan Nagel recommends setting both "macro goals" and "micro goals". In a comment on a different post he says that learning just to pass a language test is not very motivating. The conclusion I draw from this is that you should be able to define at least one macro goal and a few micro goals before you start learning Japanese. (You should also have these for German, by the way.) If you can't think of any goals, you need to think a bit harder about why you want to learn the language.