Hello! I think you want to know about honorific expression,isn'tThis is also very difficult for us． 一緒にいかがですか？（It is used when you invite your supervisor or someone who is not so friendly） →もしよろしければ一緒にいかがでしょうか？ is the best for your boss．（It means that ＂I would be grateful if I could invite you．＂） 一緒に行きませんか？（for your colleague） Would you like to come with me? （a little bit polite expression,I don't use this when I invite my friend.） 一緒に行かない？(for your friend，family，friendly colleague) Do you want to come? or Let's go together．

A small addition to takasan's elaborate explanation. いかがですか in casual form is, どうですか　So, from most casual to polite / business polite will be: Using どうですか 今日一緒に映画に行くのは/映画はどう？ friends 今日一緒に映画に行くのはどう/いかがですか？this is not casual 今日ご一緒に映画（に行くの）は如何ですか？Here you would definitely need ご+一緒 speaking to your boss/clients Speaking of a colleague, it also depends on how close you are with your colleague whether to use 如何 style or not. Then, we also have casual 行きますか？　VS　Business polite行かれますか？ 行きませんか？ VS 行かれませんか？