** Makeup company Elf Beauty's ELF.N shares down about 2% at $122.10

** Deutsche Bank downgrades ELF to "hold" from "buy" rating

** Brokerage says social media commentary around Elf and Rhode has turned increasingly critical in recent weeks

** Raises PT to $128 from $121

**"We continue to see room for sizable expansion across both the Elf and Rhode product lines, particularly overseas," brokerage says

** 13 of 16 brokerages rate stock "buy" or higher, three "hold"; their median PT is $135 - LSEG data

** Including session's moves, ELF stock is largely flat so far YTD

(Reporting by Anshi Sancheti)

((Anshi.Sancheti@thomsonreuters.com))