You have 2 options:
- Use a bigger subnet (e.g. instead of /24 use a /23)
- Add another VLAN and configure the router/firewall to forward required traffic.
Solution 1: You will need to change the network mask on all machines connected on the current VLAN. Because you are using only a slice of 192.168.0.0/16, you can grow your VLAN to have a maximum of 65534 IPs. For example if you want to use a /23 instead of /24 and keep the current assigned IPs, all you need to do is to change the netmask from 255.255.255.0 to 255.255.254.0. You will have all IPs in the range 192.168.0.* and 192.168.1.* in the same VLAN. This change must be done on all hosts and on router too. If you are using DHCP it will be much easier.
Solution 2: This solution has the advantage that you can increase the security by separating the traffic of some computers from the traffic of others. You can (and, probably, should) have a firewall between the VLANs. Another advantage is that you do not need to change anything on the machines in the original VLAN. To create another VLAN you will need to have either a switch with management (that supports IEEE 802.1Q), or multiple dump switches at least one for each VLAN. In the router you will need either to have support for VLAN encapsulation (IEEE 802.1Q) or you will need an ethernet interface for each VLAN. For the new VLAN you can assign any prefix you like, that doesn't intersect with the current one. e.g 192.168.1.0/24 or smaller ones, like 192.168.1.0/25.
No mater which solution you chose, having most of the IPs configured by DHCP will help you manage IP allocation easier.