How to make several class C networks with the same gateway

I am not strong in subnets and am now in a bit of a pickle.

When I started here they were running 10.10.10.x with everything on this network. We have grown much larger and there was a lack of planning in the beginning.

We have a sonicwall that now has 3 interfaces on it, 10.10.10.x, 10.10.1.x and 10.10.2.x these are physically assigned, they all work, they all route.

I am now faced with 2-3 more subnets inside our network, perhaps more in the future.

SO....

It makes more sense to me to make a class B and then build some class Cs inside that. However I am not familiar on how to do this.

What would be nice, is to have a single gateway assigned to a physical interface on my sonicwall and just to adjust subnet mask and IP on the devices,

As an example.

All Switches and routers in 172.16.0.1-254
All Servers in 172.16.1.1-254
All Workstations in 172.16.2.1-254

I have to apologize, I have been an IT guy a very long time, but mostly in the small business arena and 95% of them run class C networks in the 192.168.0.x range off some type of Linksys box.

I have the ability to make a new interface on the sonicwall and migrate all the other stuff over to the new schema.