Do "Gold per 10 seconds" items stack?

Solution 1:

Gold per 10 items stack with each other, however, the same gold per 10 item does not stack with itself. So, you can have a philosopher's stone and a heart of gold, and you will now have 10 gold per 10 seconds. You will only get 5 gold per 10 if you have two philosopher's stones.

Two gold per 10 items will not burn your income, especially when you got both of the gold per 10 items early on, so their effects last for a longer duration until you upgrade one of them such as the philosopher stone -> shurelia's reverie.

Solution 2:

Individual gold per 10 items do stack. Say you have an Avarice Blade, Heart of Gold, Philo Stone, and a Kage's Pick. You would get 20 extra GP/10.

At one time (7-8 months ago) you could get more than one Philo Stone and the gold would stack, but they realized how ridiculous a support champion would be with more than one item with stacking gold effects and changed it so that only the first item counted.