How can I get two calculators going?

The quickest, simplest and arguably most correct way of doing this is using the open command in Terminal.

In a new window, run the command

open -na Calculator

This will open a new (-n) instance of the application (-a) Calculator.

If you want to have this handy at the click of a button, you can type the following commands into the Terminal, and it will create a shortcut named calc or calc.command on your desktop that will always open a new instance of Calculator

cd ~/Desktop
echo open -na Calculator > calc.command
chmod +x calc.command
exit

Mind that you don't already have a file named calc.command on your desktop, or it'll be deleted!

The open -na Calculator answer is good. When I needed to do this before, I wrapped it in an Applescript:

 do shell script "open -n " & quoted form of the POSIX path of the (path to the frontmost application as Unicode text)

This detects which application is currently in the foreground and starts a new instance using the open -na method.

Save this script in the Applescript Editor as something like "Run another instance" and put it in your /Users/${USER}/Library/Scripts directory. You will then find it under the User Scripts Menu (which you may need to enable):

Simply bring the calculator to the foreground, then select this menu item and you'll get another calculator instance.

You can run as many as you like and even without duplicates of the application.

Double click the application to open one instance, e.g.

/Applications/Calculator.app

Then double click the executable to open a second instance
(you will have to ctrl+click or right-click the application and select "Show Package Contents" to navigate to the executable):

/Applications/Calculator.app/Contents/MacOS/Calculator

In this second instance a Terminal window will open to run the executable. Don't terminate it, or you will terminate the second instance of Calculator running.

Double clicking the executable lets you open as many instances of Calculator as you like (meaning I don't know the upper limit).