It is the same number of appeals registered in the entire period of the London Games in 2012.
Appeals from 17 Russian rowers, as well as three Olympic medal-winning swimmers, have been adjourned.
The Russian weightlifting federation is also fighting a team ban.
Cas is an independent international institution that arbitrates on sport-related disputes.
Individual sport federations banned the competitors after the International Olympic Committee asked them to rule on which Russian athletes can take part.
The IOC asked the governing bodies to exclude anyone who has previously served a doping ban or implicated in a recent report into state-sponsored doping in Russia.
The International Weightlifting Federation excluded all eight Russians entered for Rio last week.
Two of the eight-strong weightlifting team had already been banned for prior doping violations, and another four were named in Dr Richard McLaren's report into the issue.
Swimmers Vladimir Morozov and Nikita Lobintsev were also implicated in the report and are seeking to overturn their bans by swimming's governing body Fina, claiming the suspensions are "invalid" and "unenforceable".
A decision on their participation, along with the case of Daniil Andrienko and 16 other Russian rowers, will be made on Tuesday.
The next steps in the case of London 2012 200m breaststroke bronze medallist Yulia Efimova will also be decided on Tuesday. Efimova is banned from Rio for previous doping offences.
Cas said the Russian Weightlifting Federation's appeal against its suspension was likely to be dealt with on Wednesday.
The World Anti-Doping Agency had recommended all Russian athletes be excluded from Rio 2016, but weightlifting and athletics are the only sports to have imposed a blanket ban on competitors from the country.
An earlier Cas ruling - known as the Osaka rule - blocked attempts to ban athletes who had already been sanctioned for doping offences, saying there should be no  double punishment.
The Court of Arbitration for Sport has handled 11 appeals - predominantly from Russian athletes banned for doping - during the seven days it has been at a temporary base at the Rio Olympics.