回答
He dropped by our company,asking to meet with Mr.X.
He dropped by our company to ask to meet with Mr.X.
He dropped by our company asking to meet with Mr.X.
He dropped by our company for asking to meet with Mr.X.
He dropped by our company with asking to meet with Mr.X.
This is not a piece of advice to you I'm talking to myself for my practice of writing skills. on the site, I suppose it would be a common knowledge that on this screen right crick of the mouse would lead Google Translation start to work. if you have clicked "日本語に翻訳(T)" you could read the sentences in Japanese language.
as I haven't any interlocutor in English but GT, so I have a belief that the sentence would be comprehended if GT could translate. but in the conversation I'm not sure it's natural or not. as a reference only.