After testing, I answered my own inquiry.
It is possible to do this. Use a bridged network device on the VM with no VLAN tag.
Then inside the VM, linux in my case, create a network configuration with multiple VLAN tags on a single network interface.
As long as the tag is allowed on the trunk of the host interface, the vm tag will pass through directly to the host and then network unchanged.
This way multiple virtual NICs are not needed on the VM. Only one NIC is needed with configuration for multiple VLAN tags.