Build the meal around inclusion, not exceptions
The easiest way to make a mixed team meal feel awkward is to treat vegetarian diners like a side note. A stronger approach is to make sure the order naturally includes dishes that appeal across the group.
That way the vegetarian-friendly options feel like part of the meal, not a separate box to check.
Choose overlap where possible
Menus work better for mixed teams when there is overlap: dishes that vegetarians can enjoy, dishes meat-eaters recognize, and enough variety that the organizer does not need a second restaurant to cover the table.
This is one of the reasons Thai menus can work well for group planning.
Use direct planning for larger teams
The larger the team, the more likely it is that dietary preferences will affect the whole meal structure. Direct planning makes it easier to confirm what proportion of the order should be vegetarian-friendly and how to keep the menu balanced.
That is more useful than guessing and hoping the table sorts itself out.