There is probably nothing in the c++ compiler that prevents you from writing many classes into a single source file.
But its not the correct way of doing it of course unless its really trivial classes. The nice thing to do is to have class1.h, class1.cpp and class2.h, class2.cpp.
Leafpad has no problems with letting you edit those files, one at the time. But if you want to switch quickly between each file, you either has to start multiple instances of leafpad or find an editor that supports multiple text-buffers. Geany is probably a good next step.
You also will have the problem of quickly compiling and linking many sourcefiles into a program, so you should also learn to write simple GNU Makefiles.