To modify the source code you'll have to find where it clears. This usually means following out functions in the source. Typically it all starts in main(). This can time consuming to do but you get faster at it. Then to compile it you need Visual Studio 2008, and the directX runtime, but that is usually where people give up. Using a different version of Visual Studio has incompatibilities that would have to be changed.
Back to your original question though you can do it with a canvas and the paste action. Basically every frame paste all the objects you want to draw. There may be features that make it easier but I don't mess with Construct Classic any more so I don't know them.