The production will move to a still to-be-announced venue and reopen in March.
Boggess will lead a master class on March 11.
Dee Dee Bridgewater, Bill Irwin, and Nellie McKay will also be on hand to perform.
Guests will also include Jenny Powers, Donna Bullock, and Rachel de Benedet.
The disco musical explores the life of Imelda Marcos.
The work of late pop/folk musician Dory Previn will be featured at the event.
Youngsters at accredited schools will be able to reenact Broadway's story of Simba beginning 2015.
The new "Married Couples" episode will also include Kat Nejat and Ben Thompson.
The spring performances will be broadcast on PBS.
Foster is now performing at Broadway's Schoenfeld Theatre in The Bridges of Madison County.