I think you might get better responses in the Hardware forum. I'll move it there now.
Think an i7-5960X, overclocked to around 4.2 GHz, 64 GB RAM, a GTX 970 video card, a Samsung M2.941 SSD for OS & programs, 3+ Samsung 850 Pro SSD's in Raid0 or better for media cache & previews and several (5+) Samsung 850 Pro SSD's in raid3 for Media on an Areca ARC-1883ix-12/4G raid controller.
8 to 16 angles is a lot!
What are the camera settings that you are using? (size, frame rate, etc.)
Each video stream requires I/O. Having a very fast disk system is going to be critical. I would avoid the complications and dangers of RAID and get one of these: AnandTech | Intel SSD DC P3700 Review: The PCIe SSD Transition Begins with NVMe
It will provide exceptionally high throughput, less likely to have issues you may get with RAID, and is a neat single device solution. After the disk I/O you will need lots of memory, 8GB is just not going to cut it, I would aim for 32GB minimum.
Alternatively look at clever ways of producing your edit which doesn't require ever camera angle to be loaded at once. Then create separate sequences for different times in the project. This will save you hardware costs.
Unfortunately using PCI-E slots for storage is often not the best idea for media content creation applications with GPU acceleration. Current boards slots are often a premium especially if you need to add a 2nd video card and or I/O cards later to the system for Davinci for example. You can run 2x SSD drives in raid 0 for around the same price as the PCI-E SSD drives and also get a larger volume size. The speed is close to or above 1GB/s and more than enough to handle that many layers of H264. You definitely need more ram. Multicam uses allot more ram to function especially with GPU acceleration. Even 32GB may not be enough but your platform may not support more. What CPU do you have? The CPU threading is really going to be the limiting factor. CC_Merchant is right about the 8 core. You would should have that for that many streams in multicam. Even that may not be enough, Multicam is not very efficient currently with ram or processing resources compared to standard mode.