Ask HN: Help Desk outsourcing for small co?

We manage it in-house now and have for years. It works well but there are times when it doesn't work so well. A specific example is when a customer is browsing our site on a Friday afternoon and they want to call/email/chat. When the last person leaves the office, it might be 12-24 hours until someone gets back with the user. We'd like to improve upon this reaction speed without having to hire another employee.

Ideally I'd like something that has chat, phone, and email (tickets) support.

Any suggestions?