Potassium's RDI is 4700mg per day. Most people get like half of that because most people eat a depressingly small amount of the whole foods that are abundant in it. Barring other issues, you probably wouldn't experience adverse effects at levels significantly higher than the 4700mg, particularly if you were balanced with your other electrolytes.
The reason they're so careful with non-prescription potassium supplements is that overdose and induced hyperkalemia is REALLY bad -- like cardiac arrest bad. Most vitamins and minerals you can down grams and grams extra of with no negative repercussions outside things like laxative effects with magnesium; several extra grams of potassium might actually kill you. Thus, they put small amounts in OTC supplements to make it so you have to be REALLY stupid to OD.
Easiest way to get more potassium is incorporate more potassium-rich foods into your diet. Despite being so broadly associated with the mineral, bananas aren't a particularly rich source on a per-calorie basis; stuff like spinach and broccoli is way more potassium-rich, along with most "green" vegetables. I believe some other fruits like apricots are also extremely abundant sources.
Barring that, if you use salt as a condiment, consider switching to a blend that includes KCl along with the NaCl (or making it yourself). If done in good ratios, it doesn't really sacrifice any of the "salty" flavor but can do wonders for maintaining better electrolyte balance.
