New generation of torque converter automatic transmissions (AT) include a large number of gears for improved fuel economy. Control requirements for such transmissions become more demanding, which calls for the development of new shift optimization and analysis tools. This paper presents two contributions to the field of transmission dynamics analysis: (i) bond graph method-based shift transient analysis, and (ii) deriving a unique set of conditions for beneficial use of a third (normally-open) clutch for any upshift or downshift, with emphasis on inertia phase. The derived conditions are examined on an example of 10-speed AT based on the clutch torque input trajectory optimization results. The examination results point out that the extra clutch has a potential of significant performance improvement for any single-transition upshift in the inertia phase, in terms of reduced vehicle jerk RMS value due to the suppressed inertia bump effect. The shift quality improvement is possible in the torque phase, as well, but it is of much smaller extent when compared to that related to the inertia phase.