Its not the number of support systems that matter but quality and effectiveness which counts. People have stuck with one support system and excelled.

You may have as many ports open as you wish but then people providing supprot they need to be efficient and its always better to streamline your resources than to spread and scatter them.

I would suggest prioritising resources for support.
Provide e-support thru helpdesk from say kayako or similar.
Do not provide e-mail support. Its out dated now. Much faster and better avenues there. Telephone support will help nothing better.
Telephone support may be good as backup just incase your one systems fail but prefer e-support systems from helpdesk and if you have money to affor, you can contract with such efficient server management teams unless you have your staff. These teams have average response time of 30 mins though usually they sort all within mins.

Thomas