in addition; "computer chess games are getting cheaper all the time; furthermore, their quality is improving"; "the cellar was dark; moreover, mice nested there"; "what is more, there's no sign of a change"
You use moreover to introduce a piece of information that adds to or supports the previous statement. She saw that there was indeed a man immediately behind her. Moreover, he was observing her strangely. in addition - used to introduce information that adds to or supports what has previously been said