There’s an advantage to being big: Sometimes it will get an organization special services from a supplier not offered to smaller companies.

That’s true for Hewlett-Packard Co., which until this month had a suite of premium PC support services reserved for its biggest customers.

But on Thursday the company said it is throwing open the doors for mid-size and large enterprises as well.

Starting Aug. 1 the HP Priority Services are be available to organizations with a minimum number of Hewlett-Packard tablets, desktops, thin clients, laptops or point of sale devices under warranty with the goal of aiding in-house support staff if they’ve run out of ideas for solving a problem.

“We wanted to make this available for many accounts, not just exclusively for the very large ones,” said Alan Buckner, HP’s director of global accounts for service and support.

Priority Services comes in two offerings:

–Priority Access, for organizations with at least 250 devices, offers round the clock access to highly-skilled technicians. They don’t do basic triage — that’s expected to be done by the in-house help desk. These technicians want to know what the symptoms of the problem are and what the help desk thinks the issue is. If that’s reasonable, the HP tech will expedite the solution.

Often these calls are about hardware, Buckner added, because the in-house staff have already looked eliminated the possibility of a software problem.

–Priority Management, for organizations with at least 1,000 devices, includes all services of Priority Access plus assigns a global support manager who will part of the HP [BYOD doesn’t mean closing help desks