Can I invest in portfolio companies that are competitors?

Yes, but it can hurt your reputation with founders and even if they allow you to invest, they'll be unlikely to share key updates out of fear that you might share it with their competitor. Also, it will be pretty involved for you to manage this conflict and the information. You probably need to take this to the IC on both funds etc… Tl’DR Though it's technically possible, in most cases it's not worth it.