Run multiple instances of El Capitan on a single Apple laptop?
Virtual Machine

A virtual machine is a software app that emulates a complete computer. 

File System

The VM opens one big file in the host, and stores an entire file system inside. That file system includes an OS to boot such as BSD, Linux, MS Windows, or Mac OS X. Apple’s license permit Mac OS X to be run in a VM only when hosted on a real (physical) Mac. 

Easy Backups

One benefit of having an entire guest file system stored in a single file on the host OS is easy backups. Attach an external hard drive and copy over the single (but large) VM file to capture a snapshot. Note that you should exclude these VM files from your Time Machine as their size will overwhelm your Time Machine storage. To exclude them, use the Privacy tab in the Time Machine pane of System Preferences. Also, your VM app may offer a setting to exclude from Time Machine.

Entire Desktop Within a Window

The VM runs in a window like any other app on the host computer. Inside that window will be an entire other Mac desktop. You may find it less confusing to run the VM in full-screen mode, so the virtual desktop takes over the entire screen thereby appearing to be a second Mac. See the System Preferences panes for mouse, trackpad, and Mission Control gestures for switching between full-screen apps.

I regularly work this way as a software developer. Each development project lives in its own virtual machine. This works so well that I set the virtual Mac Dock to right side of the screen while the real Mac Dock is on the left, so I can differentiate as a reminder while I work. 

VM Products

The main VM products available for Mac hosts are :


Parallels
Fusion by VMware
VirtualBox by Oracle


See these comparisons. 

All three are solid products, actively maintained and improved. All work surprisingly well on a Mac. All run various operating systems as guest OSes including BSD, Linux, and many more.

The first two directly support installing Mac OS X as a guest OS. Just point them to Apple’s installer app for any of the more recent versions of Mac OS X going back at least to Mountain Lion. VirtualBox is not so simple, apparently requiring some tricks to install Mac OS X as a guest.

The first two listed products have put much work into features to integrate the guest OS with the host OS. I find those features unnecessary and even counter-productive. Fortunately you can disable much of that integration.

Networks

The network can be shared with the host computer, using same IP address. Or VM can present its own IP to the network, appearing as a second computer. Thirdly, the VM can be isolated from the external network. Your choice.

Limitations

VMs work surprisingly well overall. Every version of every VM tool I have used always has some some glitch or another, but never a show-stopper.

One major limitation is a lack of support for hardware-accelerated graphics. So playing videos and games performs poorly. Overall usage can seem sluggish as menus and windows do not draw as quickly. I have verified this is true for all three listed products when running Mac OS X as a guest OS, as of 2015-10.

I do not know about the support of multiple monitors. I have used Parallels versions 8, 9, 10, and 11 successfully with multiple monitors on the host Mac, but the virtual machine knew only of one monitor at a time. 

Requires Much Memory

I use a MacBook Retina 15" laptop with either an HDMI monitor or a DisplayPort monitor. I have 16 gigs of memory installed. The VMs do require much memory, and may not work well on Macs with two or four gigs.

Requires Storage Space

Each VM file can be large, usually starting at a few gigs and rising to several tens of gigs. Plan accordingly. Each product listed has a feature to reclaim empty space that may accumulate within its' VM file.