Hi, This is an interesting topic but I fear that I may have a discordant view. English, the Scots variant, is my mother tongue and I find that I appear to be different when I have conversations in Welsh. I become hesitant, tongue tied and quiet. My range of topics becomes circumscribed and my expressions become simpler and more hackneyed.I lose many of my debating (or perhaps better described as arguing) skills when I am in my second tongue. Perhaps as I improve in fluency these effects will lessen but I think it unlikely I will ever be able to match my abilities in my first language - I don't have enough time left living, to compete with the half a century I've spent immersed in my English culture.
Sometimes I think it odd that new friends I have made, in my Welsh speaking life, do not know the real me. They know someone quieter, less expansive in speech, less argumentative, less witty and less cultured. Often it is a surprise to me that they bother.
I suppose I do not think that there are different me's, I am the same person in whatever language, but this may be more or less visible because of the effect of language on behaviour, communication and understanding. Clearly we all change and develop over time and our experiences alter us; moving to a different country, learning a new language, meeting different people all help us change and develop. New experiences are overlaid on old ones but don't cancel them out, the person we are will hopefully change but we will always remain the same, single person.