"let me answer, if I may". This is a polite way to get everyone's approval, and to have them listen to what you are saying. "I will give my opinion, if I may". Same permission being asked for as above. You could say, "I have a different opinion, if you don't mind"..... (you don't want to be argumentive). "I know that some of us here want to do something else during our retreat this year. If I may, I'll give you our suggestions".

"If I may (do so)" is how you can understand it. It's usually a precursor to some polite action such as pouring a drink, or opening a door for someone. You're referring to the action you have begun.