Variables in Google getRange

I have a simple need to copy a range (E4:G4) and paste it X rows below, determined by the value of a cell, C2. I think I may be misunderstanding the offset function since when I run the routine, I get a "range not found" error, presumably because "dest" is not defined properly. Any suggestions?

function macrotest() {
  var spreadsheet = SpreadsheetApp.getActive();
  var rowoffset = spreadsheet.getRange("C2").getValue()
  var cell = spreadsheet.getRange("E4");
  var dest = cell.offset(rowoffset,1) 
  spreadsheet.getRange(dest).activate();
  spreadsheet.getRange('E4:G4').copyTo(spreadsheet.getActiveRange(), SpreadsheetApp.CopyPasteType.PASTE_NORMAL, false);
};