No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Too many accounts with balances is referring to your number and/or percentage of accounts that you have a non-zero balance currently reported on. People have reported seeing that negative reason statement both if their percentage of accounts with balances is high or if their number of accounts with balances is high. For example, take 2 different people. One may have 6 total accounts on their credit report, say 2 open loans and 4 open credit cards. Another person may have 24 open accounts, 2 similar loans and 22 credit cards. The first person with only 6 accounts may be able to have 2 of them with balances (the 2 loans, for example) but if one of their credit cards reports a balance and they reach 50% of their accounts with balances they may see that reason statement (at 50%). The other person would need 11 of their accounts to have a balance in order to hit that same 50% number, but they may see that reason statement show up when they get to 6 or 7 of them with reported balances. The reason here is that the algorithm may be looking at just the number of accounts, not percentage. Perhaps 6 is "ok" but 7 creates that negative reason statement. These are just numbers I'm throwing out here for discussion purposes.
'high balance' as you mentioned has nothing to do with 'number of accounts with balances.' As you stated, high balance is simply the highest balance ever reported on that account. It can be a good thing or a bad thing. It's good if your current balance is low, say $0 or a few hundred bucks, but your high balance is several thousand dollars. This shows that you've been able to run up a high balance but pay it down, which is a sign of a responsible borrower. If your current balance is high, say you owe $3000 and your high balance is $3500, that isn't such a good look, but it really depends on the length of time it's been there. If it's just 1 cycle, no big deal if you're the type of person that runs up a high balance every month and then pays it right off. Where it becomes a risky sign to a lender is if your current balance stays high, perhaps around your high balance for a period of months on end, as it shows for whatever reason you aren't paying down that debt very quickly.
Hopefully this information helps!