If you are looking for more throughput/bandwidth than a single NIC can give you there are several ways to do this. The simplest ways are combine NICs in a port-channel (LACP) or put each interface in a different IP subnet. What do they give you?
Pro: 1 large capacity virtual NIC
Con: The directly connected device must support configuration options for a Port-channel, and it must be of the same type, as there are several different types.
--Different IP Subnet--
Pro: Port-channel supported device is not necessary (low-cost, ubiquitous)
Con: An IP router is needed to route packets from one subnet to the others.
If you choose the second option because you have a low-cost, basic switch, heavy use devices must be placed on different subnets to keep the traffic separated. Its difficult for a low-cost switch to help you accomplish this with certainty. If you have multiple low-cost switches, you could use one for each subnet and use the appliance as the router.
Do you have routing turned on in OpenBSD (ip.forwarding=1 in sysctl.conf), or on another device? I can't tell from the info given.
So, what switch/device(s) are you plugging your appliance into? What features does it support?
If it supports VLANs and basic IP routing, then subnets are an option. This means that you can configure routing on the switch/router and your appliance doesn't need to do that work. You setup a VLAN for each subnet, a router IP address for each subnet on the switch, and put a different interface on your appliance on each subnet.
If your switch/device supports port-channeling and you can get it to work, most likely it won't be a bottleneck for the attached devices (unless it is really dated). You don't tell us why you need to run multiple NICs specifically.