A good question that comes up fairly frequently. It sounds reasonable. Maybe it would be quite efficient. I used to be interested. My simple answer today is “bad idea”. And now for the more nuanced answer.
Firstly, it depends a little on the languages concerned. I experience zero confusion between my French and my German. So two such different languages could be learned at the same time and would be unlikely to cause you trouble. On the other hand, recently I have been experiencing some considerable difficulties trying to keep my Spanish and Italian in separate dictionaries in my brain. So the similarity of the languages would be a factor.
More importantly for most adult clients, life is quite variable, time is short and there are many demands on our time. The struggle is to maintain the motivation to keep investing the time. Language learning is a marathon not a sprint. The motivation comes from seeing progress. Given you have only so much time to invest in language learning, to split that over two languages is likely to lead to more frustration and disappointment than progress and delight.
In short, I do not recommend it. If it comes as any consolation, I once speculated if learning six languages simultaneously was a good idea. So at least this person has a 5/6ths less bad idea than the one I had.