Given the size of Boeing aircraft, it would be difficult to have a flight department made up of only Boeing aircraft.
When I worked for Boeing Wichita, I took a company trip on a Boeing company airplane. The airplane was a Cessna Citation 3, Model 650. At that time Boeing owned/leased about 3 Citation 3s.
When I traveled on commercial airlines on a Boeing trip, I sometimes flew on Airbus aircraft.
I received my PPL in the Boeing Flying Club. They used C172, C182s.
Boeing Flown: 701,702,703;717;720;721,722;731,732,733,734,735,737,738,739;741,742,743,744,747SP;752,753;762,763;772,773.