Yes, the limit is six pets as stated in the Municipal Code, Section 14-53, Keeping of More Than Six Pets:
The keeping on any premises in the city of any pets in any number exceeding six in aggregate is prohibited unless the pens, stalls or other enclosure facilities for keeping the same shall be so located that pets cannot come within 100 feet of any dwelling or business building, owned, used or maintained by any person other than the keeper, or 500 feet of any foodservice establishment or food processing establishment, regardless of ownership or occupancy of such establishments.