Brookline has formed a design team to review a proposed 127-room hotel along Route 9 on property that includes the former Red Cab headquarters. The Bridgewater-based real estate firm Claremont Cos. is seeking to build a Hilton Homewood Suites hotel at 111 Boylston St. that would cater to guests seeking lodging for several days. The hotel would be five stories tall along Route 9, but would step down to four and then three stories at the rear of the property, which abuts the MBTA’s Green Line tracks and a residential area. Proposals by Leggat McCall and then GLC Development Resources LLC to build medical office buildings on the long-vacant site have fallen through in recent years. Elias Patoucheas, president of Claremont Cos., told the Planning Board at a meeting in late June that while the previous developers fell victim to a bad economy, that won’t be an issue for his firm, which already has money for the project in the bank. Most of the parking will be underground, and the hotel will have a pool, lounge, meeting rooms, and fitness rooms. A design advisory team appointed by the Planning Board will begin reviewing the project this month.