If you are scheduling one rep against a prospect, the world is your oyster. Every scheduling tool on the market handles this. Pick a slot, book, done.
If you are scheduling three internal people plus the prospect, things go sideways. The rep, the solutions engineer, the director, and the prospect all need to be on the same call. The intersection of four calendars is usually a much smaller set of slots than any single one. Show the prospect the intersection and they might only see two slots in the next week. Show them a single rep's calendar and they see 30 slots, but then the booking requires the rep to manually loop in the other two people, who then cannot make it.
Most tools handle this badly. They either ignore the other attendees entirely, which produces the "let me loop in my colleague" email that adds two days of delay. Or they do show the intersection, but the intersection is so sparse that the prospect bounces.
The trick is a combination of priority and flexibility. Not every internal attendee is required. The rep has to be there. The director is nice to have. The solutions engineer can be optional for the first call. If you encode that hierarchy into the scheduler, it can show more availability by dropping the optional attendees from the intersection when needed, and only requiring them when they are really required.
The other trick is letting the prospect pick a slot that is tight for the internal team, and then handling the conflict internally afterwards. "The prospect picked this slot, the rep is available, the director has a soft conflict. Here is the conflict, resolve it." Most of the time the director can move their other thing. You get the meeting booked. If you had required perfect intersection, the meeting would not have been booked at all.
This kind of thing is where custom schedulers beat off-the-shelf tools. The logic is specific to how your team works. A generic tool does not know which attendees are required and which are optional. A custom one can, and the difference in meeting booking rate on enterprise deals can be significant.