No it does not, just something around a dozen more and if you could call a dozen many, then - "many more." ))
Actually in my opinion it does have an exact meaning, though the meaning itself is "about ten more". The word "десяток" itself means ten, not dozen, so it's not something around a dozen, but around ten instead; the preposition "с" stands for "around", compare еще десять названий and еще с десяток названий.