Collective webmail application

We are in need of a webmail application which can be used bij more than one person on the same account - at the same time. Simply put - our customerservice e-mail adres is growing, so we need more people working in the same account at the same time to be able to reply all mails. A ticket system is only an option WITHOUT the ticket nr aspect. Our customers are sensitie mothers who do not want their communication with us 'to be any number'. We wish to enhance and keep the personal communication. A ready available application is prefered - in that case a mutual agreed fee will be paid for the advise (if we choose the suggested application).