I realize that a table is not assigned when the reservation is made. What I was trying to say is that, particularly at a busy time, there might not be capacity for another party of nine (so trying to make a new reservation wouldn't work) but depending on the seating arrangements at the particular restaurant, adding one more to a party of eight wouldn't be a big deal since, as you say, it would be unusual for a restaurant to reach the fire code capacity. Maybe the best thing for the op to do is to make a separate reservation for a party of one as close as possible in time to the original reservation and then ask to be seated together when they check in. That is what I may do if we need to add another family member to our reservations.