(CNN) — The biggest mall owner in America says it’s time to go shopping again.

Simon Property Group, which has 204 properties in 37 states, said late Monday that 199 of its shopping centers have reopened — even as concerns grow about a second wave of Covid-19 cases in the United States and a deluge of retail bankruptcies.

It expects the remaining five properties to reopen sometime within the next week. These malls collectively have more than 18,000 stores, and according to Simon, many of them have reported better-than-expected sales since reopening.

Shares of Simon were flat in midday trading Tuesday on the news. That followed a more than 10% spike Monday as the broader market rallied.

Simon also said Monday that nearly all the stores in its international outlets (mostly in Europe and Asia) are open. The company just announced the grand opening of a new outlet mall in Bangkok.

Still, Simon has a big hole to dig itself out of before it gets back to pre-pandemic levels. The stock remains down more than 50% this year, even after the rally of the past few days.

Many malls had been struggling even before the economy fell into a recession as a result of the Covid-19 outbreak.

Consumers have been shunning big malls in favor of superstores like Walmart and Target as well as Amazon and other online retailers. That’s hurting landlords like Simon.

Simon is fighting back and trying to capture its own piece of the lucrative digital commerce pie. The company announced a joint venture in October with Rue Gilt Groupe to launch an online site for Simon’s outlet shopping centers.

But Simon faces several legal challenges as well. The company had agreed to buy rival Taubman Centers in February for $3.6 billion. Then the coronavirus outbreak ground the US economy to a screeching halt. Simon terminated the deal earlier this month.

The two companies are now suing each other. Taubman said Simon’s decision to end the merger is “invalid and without merit” and Taubman shareholders voted to approve the deal last week.

Simon is also suing mall stalwart Gap for failure to pay $66 million in rent for the more than 400 million locations it leases from Simon. The Old Navy and Banana Republic owner has been hit hard by Covid-19, but shares have rallied in the past few days on optimism about store reopenings and a new deal to sell a line of Kanye West’s Yeezy apparel.

The bankruptcy of mall anchors such as JCPenney, J.Crew and Neiman Marcus could also hurt Simon and other mall operators as they lose tenants. But Simon is trying to stop the bleeding.

In February, the company agreed to buy a 37.5% stake in another bankrupt mall retailer, fast-fashion company Forever 21. Marketing company Authentic Brands and fellow mall owner Brookfield Property Partners bought the remainder of Forever 21. This consortium agreed to buy bankrupt Aeropostale in 2016, too.

Simon, Brookfield and Authentic Brands are also reportedly looking to buy JCPenney.

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