In 1996, Stares introduced monotonically semi-neighborhood refining (MSNR) spaces and showed that well-ordered neighborhood (F) spaces are MSNR spaces. In this talk, the question of whether MSNR spaces have well-ordered neighborhood (F) is explored. We show that MSNR spaces have well-ordered (F) and hence are monotonically normal and hereditarily paracompact. MSNR spaces are also shown to be lob-spaces. The relationships between MSNR spaces with other monotone covering properties will also be explored.