The IOC has already invited 169 Russians to the Pyeonchang Olympics under a neutral flag, but may now be forced to allow in athletes it deems dopers, eight days before the Games begin.
It wasn't immediately clear how many of the 28 Russians would now seek to compete. Some have already retired from competitive sports.
Those reinstated at the Sochi Olympics include skeleton gold medalist Alexander Tretiakov and cross-country ski gold medalist Alexander Legkov. Russia won't win back some medals, such as in the men's 4-man bobsled, where two crew members were disqualified and two reinstated. Both of the gold medal-winning two-man bobsled crew remain banned.
The IOC last year banned 43 Russians over doping offenses at the Sochi Olympics, ruling they had been part of a scheme to dope.
The Russian director of the laboratory which handled samples for the Sochi Games, Grigory Rodchenkov, said he gave cocktails of banned steroids to athletes and swapped tainted samples for clean urine on orders from Russian state sports officials.
The Russian government vehemently denies ever supporting doping.
Three more appeals, all involving retired biathlon competitors, will be heard later.
To get the day's top sports stories in your inbox, sign up to our newsletter here