Story highlights Melania Trump is splitting her time between New York and DC

She is working to fill top positions on her East Wing staff

(CNN) It's been almost a week since her husband took office, and first lady Melania Trump still has not officially announced her own White House team. While she won't be a full-time DC resident until son Barron, 10, completes his school year at a New York City private school, a spokesperson for the first lady this week told CNN that Trump would be "splitting her time between Washington and New York for the next few weeks."

One of the big tasks on her agenda: filling the open slots of her top staff positions.

Notably missing from Trump's staff are a press secretary, a social secretary, a communications director and a chief of staff. Some had assumed a front-runner for social secretary would be David Monn, the New York-based event planner, whose website carries the slogan, " Truth is beauty, and beauty is truth ." He was responsible for the look and feel of several inaugural parties, including the candlelit dinner at Union Station the night before President Donald Trump's swearing-in.

However, the White House has been mum on Monn's future plans there. Monn has some experience with the inner workings of the White House social structure; in 2010 he collaborated with the Obama White House social staff, overseeing the design of the State Dinner for Mexico's then-President Felipe Calderón

One of the names being floated as a possible deputy chief of staff and East Wing strategist is Stephanie Winston Wolkoff, a New York fashion world luminary who spent several years helming the planning of the annual Met Gala, which is essentially the Super Bowl of the style set.

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