Originally Posted by EMAW

The 350 is a commuter category airplane. 91.531 a. 3 says that no operator may operate a commuter aircraft without an SIC, except they MAY do so if the aircraft is certificated for one pilot and the aircraft has nine or less seats. The operative word being MAY. So if they decide to use an SIC, it is logable in this situation.
Also, an SIC type isn't required. 61.55 (a) 3 says that a type rating is required UNLESS it is a completely domestic operation. Also, 61.55 (b) goes on to list the training required to act as SIC. But, 61.55 (d) says you MAY receive an SIC type, and 61.55 (d) 7 also states that a practical test isn't required in this situation.
So, IF they are willing to teach you about the airplane and CRM, and give you the flight training required by 61.55, you would be able to fly and log SIC. If you want the SIC type, you'd just take your training records and a completed 8710 to the FSDO and they'd issue you one.
Of course this is all paraphrased.