In many languages, there is an instruction called break that tells the interpreter to exit the switch after the current statement. If you omit it, the switch fall-through after the current case has been processed:
switch (current_step)
{
  case 1: 
    print("Processing the first step...");
    # [...]
  case 2: 
    print("Processing the second step...");
    # [...]
  case 3: 
    print("Processing the third step...");
    # [...]
    break;
  case 4: 
    print("All steps have already been processed!");
    break;
}
Such a design pattern can be useful if you want to go through a serie of transitive conditions.
I understand that this can cause bugs due to unintentional fallthrough if the programmer forgets to insert the break statement, but several languages are breaking by default, and include a fallthrough keyword (e.g. continuein Perl).
And by design, the R switch also breaks by default at the end of each case:
switch(current_step, 
  {
    print("Processing the first step...")
  },
  {
    print("Processing the second step...")
  },
  {
    print("Processing the third step...")
  },
  {
    print("All steps have already been processed!")
  }
)
In the above code, if current_step is set to 1, the output will only be "Processing the first step...".
Is there any way in R to force a switch case to fall through the following case?