No, that doesn't work like that.
Firstly, VRAM isn't an indication of actual computing power, and for most things, the vram on a given card is good for it.
(Say, a gtx 1050 doesn't need 12gb of VRAM because it can't run anything that would need that amount)
Anyways, no, you cannot add a 2nd card "just like that".
There is a technology called SLI, which used to let you put 2 IDENTICAL GPUS (an ASUS gtx 1080 and an EVGA gtx 1080 would work, but a 1070 and a 1080 wouldn't)
And they would both render the same game togehter. Nowadays, that technology is mostly dead, I can explain more in detail why and when that happened, but generally, it's not something you can do.
That aside, you can still put a 2nd card in your system, but they cannot both work concurrently on the same render.
You can set 1 card to run inside a VM or maybe set 1 card to render a video while the other plays a game, or even just use the 2nd gpu and more HDMI outputs, or render everything on the 2nd monitor and stuff like that, but you cannot use them to render out a single application.
SLI Support in reverse order to demonstrate, and yes, the cards must match (There were a FEW exceptions to this when there was a little rebranding, and some exceptions caused by the introduction of RGB effects on the SLI bridges themselves(weird, I know)). Officially, Nvidia is no longer making SLI profiles for new games as of January 2021.
RTX 3090
Titan RTX, RTX 2080 Ti, RTX 2080, RTX 2080 Super
Titan Xp, Titan X (Pascal), GTX 1080Ti, GTX 1080, GTX 1070
Titan X (Maxwell), GTX980 Ti, GTX980, GTX970, GTX960, GTX950
SLI (or Crossfire from AMD/ATI) means the GPUs share an identical memory pool, so 8GB and 8GB doesn't equal16GB, the same information is stored in both cards simultaneously.
Direct X 12 (Direct3D) is also capable of utilizing multiple GPUs, of any type. However, this is up to the game developer to implement.
Implicit multi-GPU is essentially SLI or Crossfire with the GPUs and requires identical GPUs.
Explicit multi-GPU does what you wanted, tossing all the GPUs into a general pool of resources so they can split up to work on the same task. In practice this is terrible as you can't exactly predict when things will get done, so you see a lot of stuttering. VRAM pool becomes the total of all the GPUs.
Sadly this never went even close to mainstream, just a few fancy benchmarks and one game only famous for being a benchmark.
VMs is another area where multiple GPUs can be handy. Still, this is only recently something Nvidia supports outside of the professional grade Quadro cards. But it would truly allow multiple people to perform very complex tasks on the same system remotely, or with peripherals directly attached. (Still a support mess though)