My underlying assumption here is that a team has a personality which can be described comparably to that of an individual.
Teams are formed to fulfill specific task, typically specified externally. For each task there is an ideal ‘team personality’ that fulfills this task best.
Team personality transformation means to change the current personality of the existing team to get closer to the ideal personality.
HEXACO is presumably not sufficient to describe the personality of an existing team completely. However, HEXACO is a good start and as an established method it might be more acceptable than a green field approach.
The HEXACO scores of the team are simply the average values of its team members.
Simple example: If all team member are fearful, anxious and consider themselves as not particular creative, it might be unlikely that this team will come up with an innovation like a ‘flying machine’ or a new type of explosives.
For each category of task, there is an ideal team personality. It is rather a cluster in the 6-dimensional HEXACO-space, i.e. some deviation from the ideal value is ‘good enough’.
Simple example: For a team in medical care, high empathy and perfectionism is desirable.
Apart from the external goal, as an important side condition, the team cohesion must be taken into account.
Simple example: Two individuals with high unconventionality and low modesty might trigger the team to split - or at least to be mainly consumed with team internal struggle instead of making progress towards the goal.
The staffing of the team is obviously the first and possibly the most important step on team personality optimization.
Simple example: You have to staff a team of seven, with six individuals already named. The personality scores, e.g. the HEXACO scores, of each individual are known. Then, for picking the seventh team member out of a given set of applicants, you might want to choose the one that moves the team personality most towards the ideal team personality.
For a given team, there is still some potential to move the team personality.
Personality traits are partially inherited, but also partially adopted according to experience.
In particular, an individual might have deviated from his or her inherited personality in some facets. All that needs to be done is to move back to this original score. However, this ‘moving back’ is often not done and needs an external trigger.