With colour negative film, in general.
Ever so slightly over exposing, will reduce grain size, or in other words make the negative harder to focus on an enlarger, but only a miniscule bit. I'm talking of rating a true 125 ASA film at 100 ASA as a maximum change.
In an industrial photographic studio with it's own industrial photo lab at one end, we had very tight control over C41 processing and were effectively processing C41 film right on the parameters set by Kodak. With a very slight over exposure of C41 film and dead correct processing, vibrant colours, great shadow and highlight detail were standard.
Keeping your subject brightness range (SBR) at around 5 stops from shadow to highlight extremes, is the other step we used to end up with eyepopping prints. The film was saturated with colour and glowed wonderfully when printed, it was often a pleasure to print these negatives.
SBR is important at the taking stage and many times it is the deciding factor in how punchy your end RA4 print will be.
By all means experiment, but think of the experiment starting with your SBR at the film exposure stage, then modify (if you desire) your later steps in the separate film exposure, film developing and colour printing stages.
Drew is correct, choose the appropriate film for your intended final outcome, or intended subject.
I have pushed C41 film, usually by around 2 stops, yes you will end up with higher contrast (punchier look) shadow detail goes out the window as does highlight detail. Nothing wrong with that, it's different, often gets attention and is handy to have in your arsenal. You will though, sometimes end up with incorrect colour somewhere between shadow and highlight detail; it's the price you pay.
One thing I used to get with one film, was blue blacks in prints with push processing C41 film. Normally with colour RA4 printing, when your developer is going off (exhausted) the blacks don't print as black, they have a blue tinge to them. With one film, and I forget which one, push processing gave a colour crossover somewhere in the film curve and I always ended up with blue blacks. It was very liveable for extreme colour photography, but not too flash for wedding stuff.