Would you buy an individual stock that is already in an ETF you own?

Definitely. You typically buy ETFs for diversification in a certain sector/industry/country.

Hence, if you like a particular company and its fundamentals are strong, there's not reason why you shouldn't purchase the stock. You can continue to invest in ETFs as part of your permanent portfolio while selectively picking a few individual stocks to invest in with the remaining spare cash you have. This way you don't put all your eggs in a single basket.

Of course that happens, and this is an excellent question of Yours.

I never really check what the % of some of my single stock is within my ETFs. Normally I recommend against buying single stocks, but in reality I (still) invest part of my available funds into single stocks, which I feel is against my rational passive investing approach.

Inconsistency in practice.​​​

I definitely would, or rather, I wouldn't restrict myself to solely stocks outside the ETF even if I already own an ETF. ETF although contains stocks but it is purchased for a different reason / mentality /mindset from an individual stock.

ETFs are known to be bought for diversification and long-term / recurring investments

Individual stocks can be bought for short-term capital play, dividend yield, management of company.

Hence there are different motivations for purchasing different investment vehicles. So as long as my motivations are valid, I'd go with it.

Agreed with the other responses.

Look at the stock's composition in the ETF. Some ETFs are heavily skewed towards a handful of stocks and if you were to further add on to a stock that is overweight in the ETF, that might not be a sensible choice.

Otherwise, no harm adding the stock separately if you've done your due dil.