Keeping Only Mustache
Anything that is considered to be a sign of Takabar in a society would be prohibited. Keep in mind that sign of Takabar change from one society or culture to other. So a mustache that may be considered a sign of Takabar in one society may not be allowed in that society, but it may be allowed in other society where it is not a sign of Takabar. So, ask the question to yourself. if no beard and only Mustache is considered a sign of Takabar in your culture or society, then it is not allowed. If it is not a sign of Takabar then it is allowed.