It may be possible. However I find it unlikely that one can have another language as readily and deeply holstered as their primary language.

The reason for this is that your brain goes through an acquisition phase purely for language when you are young made up of very definite and reliably observed stages. No one that talks doesn't go through this. It not only defines your language for life, but also your world in a concrete way. Like the associations used with the word "concrete" in the analogy "in a concrete way". The depth of this learning is believed to be fundamental to every individual in a pretty serious way.

So without this, untethering objects to their meanings, and 'creating a new primary' if you will, seems theoretically impossible.

However don't take my word for it though. Ask around more. Although maybe isolating and against what I personally would regard as the point of language, I love the idea of a language without prior basis in any other. It's both ballsy and creative. Please don't give up on this, and try prove me wrong.