Question : netmasking in the middle of an octet

Hi experts.  I have a network set up as 192.168.0.x with a netmask of 255.255.255.0.  This network is also connected via firewall to firewall VPN tunnels over the Internet to 3 remote locations of 192.168.1.x, netmask 255.255.255.0.  we will also add 2 more sites soon.  The firewalls handle the routing nicely, but we are approaching the point where we are running out of address at the central site.  I can’t just change the netmask to 255.255.0.0, because I will loose the routing to the remote site.
My question is, can I netmask within the 3rd octet?  Something like:
255.255.240.0
(binary of the 3rd octet is 11110000)
and make the IP addresses of the resultant networks:
            available IP addresses            
1st site            192.168.(0-15).x            network: 192.168.0.0
2nd site            192.168.(16-31).x            network: 192.168.0.16
3rd site            192.168.(32-47).x            network: 192.168.0.32
4th site            192.168.(48-63).x            network: 192.168.0.48
5th site            192.168.(64-79).x            network: 192.168.0.64
6th site            192.168.(80-95).x            network: 192.168.0.80
etc?
Is there any problem anyone sees with this plan?  Will this affect the functionality of VPN clients?  I think it is OK, but I have always set an octet of a netmask to 0 or 255, although I seems like it should work in theory.

Answer : netmasking in the middle of an octet

You can actually set a netmask anywhere in the IP address.  And, in fact, the correct network mask for the 192.168.X.X private IP range is 255.255.0.0, not 255.255.255.0 as you have been using.

Have you considered changing to a different private IP family that gives you more options?  The 10.0.0.0 - 10.255.255.255 ranges give you much greater range since it has 16M possible IPs and makes segmenting subnets much more convenient than the 192.168 range.