Couldn't you just store the function name, then when you click you check which function is then call it and update the function to which one you want?
Something like this:
function functiona(){
console.log('called functiona');
document.body.style.background = '#aaa';
}
function functionb(){
console.log('called functionb');
document.body.style.background = '#fff';
}
$('#example').on("click", function(ev){
var func = $(ev.target).attr('data-fn');
console.log(func);
window[func]();
});
$('#changer').on("click", function(ev){
//HERE you can change the function will be called based on what you want
//Here I just changed it with a simple if...
var fn = $("#example").attr("data-fn");
if (fn == 'functiona'){
$("#example").attr("data-fn", "functionb");
}else {
$("#example").attr("data-fn", "functiona");
}
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div id='example' data-fn='functiona'>Click Me to call function</div>
<button id='changer'>Change Function</button>
Here, the global variable window have your functions stored, so going through it by it's name and calling it, should work, if this name exist as a function window[stringOfFuncionName]();
This is not the best way of doing what you need (actually you didn't let completely clear your final objective), but this maybe can help.