Switching from IB to Private Banking

Hello everyone, I'm currently looking for some advice as I've just finished my bachelor's degree in finance at EDHEC and I'm starting an MSc in finance at Skema Paris. Since I started at edhec, I've done the following internships: customer advisor in first year, financial analyst in second year in a startup, M&A analyst in a small cap in third year, M&A analyst in a top 10 investment bank worldwide in fourth year. I'd now like to move into private banking, so my question is: is it possible to switch from investment banking (GS, BG, Rothschild) to private banking (EdR, Richelieu, UBS) as an intern and then convert this internship into a permanent position as a private banker or at least as an private banker assistant? I've developed some great skills through my two M&A internships.