Allen Premium Outlets is finished with construction of its original buildings and expansion of 122,000 square feet. New tenants, H&M and the only Armani Outlet in North Texas, are building out their spaces for August and fall openings.

A couple of stores coming to the center aren’t outlets. H&M and Bath & Body Works/White Barn, mainstays in most area malls, are part of the new mix.

“We believe these new offerings will speak to our current customer base, giving them new options, while simultaneously attracting new customers,” said Jay Hamby, the shopping center’s general manager.

H&M also opened last year in the new Tanger Outlets in Fort Worth. That store has a bigger clearance area than is usually found at the fast fashion brand’s other stores.

The Allen store will be a regular H&M location with its “affordable fashion,” said H&M spokesman Patrick Shaner. The fast fashion chain doesn’t operate outlet locations, though it does operate in other outlet centers around the country, he said.

H&M isn’t closing any stores in the market to open this one, Shaner said. The closest store is in Frisco at Stonebriar Centre.

The new inner ring of stores is where a Neiman Marcus Last Call store closed last year. H&M will occupy a big chunk of it — 28,350 square feet — between Express Factory Outlet and a relocated Polo Ralph Lauren outlet.

The new center area is also where the 4,526-square-foot Armani Outlet will be, next to the Tory Burch outlet. The 3,000-square-foot Bath & Body Works will open in the fall between Journeys and OshKoshB’Gosh.

Existing buildings are in yellow with new...