Please review the Q&A Usage Guidelines before posting, specifically point 3, "Quote the applicable rule from the latest version of the manual in your question."
The applicable rule in this case is RSC5:
<RSC5> A Team may handle their Robot as many times as desired during a Programming Skills Match.
a. Upon handling the Robot, it must be immediately brought back to any legal Starting Position.
i. Driver may reset or adjust the Robot as desired from this position, including pressing buttons on the Robot Brain or activating sensors.
b. Any Game Objects being controlled by the Robot while being handled must be removed from the Robot and gently placed in a non-Scored position by the Team.
c. Any Game Object in the Starting Position may be moved out of the Starting Position and gently placed into a non-Scored position by the Team.
d. During a Programming Skills Match, Drivers may move freely around the Field, and are not restricted to the Driver Station when not handling their Robot.
i. An intent of this exception is to permit Drivers who wish to “stage” Robot handling during a Programming Skills Match to do so without excessive running back and forth to the Driver Station.
Note: This rule only applies to Programming Skills Matches. Driving Skills Matches are still governed by <G17>, especially for strategic violations.
There are no restrictions in RSC5 to state that only one Driver must complete all of the "handling" interactions. Thus, this would be legal.