Can I re-compile a file with new code?

Question

I have a question. I was wondering if you could re-compile code with another piece of code. For example (theoretical):

main.c:

#include <stdio.h>

void showme();

int main()
{
   showme();
}

void showme()
{
   fprintf(stderr, "errtest, show me");
}

Compile this file to main. (So the main is compiled) After this I want to add a piece of code.

addthis.c:

void test()
{
   test();
}

Now I want to use the (compiled) main and re-compile it with addthis.c. When running it (./mainWithAddthis) should show the print 2 times.

I hope I explained it clear. Anybody an idea?