"shine more" is a correct and usable phrase in written English.
You can use it when encouraging someone to do something better than they previously did. For example, "Keep up the hard work - shine more!".
His gloom made Taylor shine more brightly.
At times you might wish the sun would shine more brightly in Mr. Berselius's kitchen.
but, in their mediocrity, they do make Impressionism shine more than ever.
It represents a potentially disastrous step backward, and it's time to shine more sunlight on it.
Now that it has, the light has been repositioned to shine more upward than outward.
"We need to shine more brightly than the neon lights of the bars.
Like parents, cooks shouldn't have favourites, but some recipes inevitably shine more than others.
Ten minutes later, the sun reappears and the red dust and green leaves shine more intensely than before.
Nowhere does the celebration shine more brightly than in a flower-shop-turned-gay-bar called Pony.
Emergencies are central to the business plans of NGOs, whose brands shine more brightly amid the suffering of others.
Its light crust of sausage allowed the egg's flavor to shine more brightly, to the benefit of the contrast, at least this once.
