The owners are selling homes in Florida, Pennsylvania, New Mexico and Colorado that were previously individually listed for a combined $46 million

For years, Robert and Miryam Knutson traveled around the country, splitting their time among homes in four states. But when Mr. Knutson came down with a “mystery virus” 18 months ago, the couple decided to consolidate to a $25 million Los Angeles mansion, and put their four homes on the market individually for a total of $46 million.

A few months later, the Knutsons concluded that the logistics of marketing four homes independently was too much work, Mr. Knutson said. So they decided to put all of them on the auction block with no reserve. On Jan. 10, Platinum Luxury Auctions will be auctioning the couple’s homes in Florida and Pennsylvania; on Jan. 12 it auctions their homes in Colorado and New Mexico.

Mr. and Mrs. Knutson said there was no fixed schedule for how much time they spent at each property throughout the year, but they rarely missed Santa Fe’s summer music and art festivals, and they enjoyed the warm weather in Boca Grande, Fla., during the winter months. Mrs. Knutson said she allowed her grandchildren to decide whether they wanted a white Christmas or a sunny one.

They said there is no favorite home. “It would be like picking a favorite child,” Mr. Knutson said. The couple added they will miss the full-time staff that cares for the properties year-round. “The staff would be alone for eight or nine months a year, and then we would appear,” Mrs. Knutson said.

Mr. Knutson, 84, is a founder, retired chairman and CEO of the Education Management Corp. His wife also is also the former COO for the company. The company, which once ran one of the country’s largest chains of for-profit schools, folded in chapter 7 bankruptcy earlier this year.

In Boca Grande, Fla., about 50 miles from Sarasota, their approximately 10,500-square-foot waterfront home was most recently on the market for $13.5 million. On 1.43 acres, it has a private boat dock, which is just a few minutes from the Gulf of Mexico, a resort-style pool and a waterfall, and more than 260 feet of frontage on the Little Gasparilla Pass inlet.

In Ligonier, Pa., just over 50 miles from Pittsburgh, their nearly 200-acre countryside estate has miles of walking trails and four pheasant-hunting fields. Its main sandstone home is about 9,300 square feet and includes a living room with dual fireplaces, a wood-paneled library and a conservatory. There is also a guesthouse with five bedrooms and a staff house. The property also has heated dog kennels, eight stocked fishing ponds and a rifle and shotgun shooting area. An annual “fox hunt” held by a local club has used the grounds. It had been on the market for $7.5 million.

In Durango, Colo., near the New Mexico border, this ranch property has been on the market for $13.5 million. It comprises four parcels in Animas Valley and offers dramatic mountain views. It has access to the Animas River, where Mr. Knutson said he and his family could fish for rainbow trout. The main house totals about 7,000 square feet, and there are additional structures that serve as guest cottages and barns.

Their 11-acre estate in Santa Fe, N.M., dates back to the 1930s. Mr. and Mrs. Knutson spent $18 million about four years ago restoring the Pueblo-style property, replacing the plumbing and electricity systems and updating the interiors, according to the auction listing. The main house has six bedrooms, and there are an additional three guesthouses, or casitas. There is also a tennis court and a large pool. It has been on the market for $11.5 million.