Any Nvidia, Intel (CPU+motherboard), or AMD GPU with a displayport technology level above 1.2 ought to work, at least with the proprietary drivers. The problem is making sure that you have the right cable connections - in some cases, active adapters and/or MST hubs may be needed to make all 4+ monitors work reliably.
If I had to recommend a GPU for you, I'd tell you to look at the Sapphire R7 250 Eyefinity Edition. You can connect two monitors to the DVI and HDMI ports, then add two or more displays using a splitter cable off the Display Port. Note that Sapphire claims it supports 3 displays in the tech specs, but the Eyefinity spec from AMD claims any GPU with that moniker supports 6. I believe this disparity is due to the fact Sapphire isn't including a DP splitter cable; such cards do work with up to six displays, as long as those displays don't exceed the total number of pixels each output is capable of pushing.
Alternatives on the Nvidia side are similar, if somewhat more expensive on average. The company really tries to push its Quadro NVS cards if you look at their official documentation, but at least in Windows I have experience using GTX cards with DP outputs to connect up to eight monitors successfully. I don't recommend that setup only because getting those cards to work in Windows was never as successful as with the AMD cards, and the many weird issues I encountered make me hesitate to recommend it for Linux, where support tends to be even more wonky.
The last thing I would like to mention is that unless space/energy is at a premium, it almost never makes sense to go with the NVS/Firepro solutions both companies offer up. These cards are expensive, inadequately cooled, and unecessary, because in reality you can just keep adding GPUs to computers and running additional displays off them without issues, so long as you have the bus connections (PCI-E normally, in this day and age). Thus in a computer with an Intel HD 4000 GPU on the CPU die connected to a DVI, HDMI, and DP out, adding two of the R7 250 Eyefinity edition GPUs above would allow that computer to push at least 3 displays on the Intel chip + 6 more on each GPU, for a total of 15 1080p displays. Any limits on that number discovered are more likely to be the fault of the OS than anything else, AFAIK.