Its not the extra NICs that will help - it is the number of HBA's you have and how they are configured.  Ideally you have enough paths to the storage so you can dedicate database access (both read and write) through on set of paths - and dedicate another set of paths to the backup storage. 

Since these are virtual machines - the path to the storage is controlled at the VM host level - and you are not going to be able to do something at that level unless these servers have a dedicated VM host and probably not even then...it would depend on how your VM environment is configured.

Striping backups is the next best alternative - as well as compressed backups.  Any of the 3rd party utilities (Litespeed, RedGates SQL Backup, etc...) will use striping in the background for you and also performs compression at the same time.  I utilize Litespeed and I am able to backup a 10TB database in about 2.5 hours - but that is on physical hardware with lots of CPUs and memory, and to an Enterprise SAN with lots of SSD drives