If a customer wishes to add another service to an existing appointment on the same day, it's best to merge the added service into one singular appointment. Merging the appointments into one will ensure that the client can checkout through one singular transaction. It will also serve as one appointment for purposes of reminder texts and emails.
First add the stand-alone appointment at the appropriate time, then when given the option make sure the checkbox to merge is checked. See the article Merging Multiple Appointments for specific instructions.
The only time a service under the same client's name should be kept separate are in rare cases where that client wants a separate transaction for each appointment.