First check that the maintenance policy specified for the system is set for user acknowledgement. If not set that first. This will let you stage the change for the service profile(s) without forcing an immediate reboot.
Then depending on how your service profiles are created simply add more VNICs to the profile or profile template (in the case of an updating template). Evacuate the VMs from the server and shut it down. Then acknowledge the change for the corresponding blade in UCS Manager. The blade will reboot and add the nic. Boot the server after and then co figure as desired in the operating system.
As far as maximum NICs, that depends on the VIC installed and the number of NICs the operating system supports. For example, the VIC 1240 provides up to 256 logical adapters (less 8 as those are reserved). Typically you put a nic on each fabric so 128 on each interconnect is what I normally design for.
VMware, windows, Linux, etc will all have their own maximum support NICs. Consult the vendor for that number.