Not a direct answer to the orignial post and just offering a personal viewpoint and experience.
Make and model printer?
I have a HP Office Jet Pro 9015.
Seemed to go through individual ink cartridges very fast. Tried to save the color cartridges by printing with just black but was not successful. (Black can be made, and apparently was being made, by mixing the other colors. )
And I also ran into the problem of not even being able to use very new ink cartridges from a neighbor who had the same model printer that had ink problems. She could not use my ink cartridges either.
Ink cartridges, a full set, increased in price to over $100 USD via big box store purchases. Normal usage being going through a set in 7 - 8 months. But then the time span started getting shorter despite attempts to conserve ink.
So I signed up for the automatic ink renewal program at $6.99 month. A year being around $84 USD.
My original set of cartridges (mailed directly to me) are still in use after several months now and no replacement cartridges have been necessary or sent. ( May be getting close though according to the printer's status report.)
However, the monthly cost is only if I use 100 sheets of paper or less. If I go over 100 pages then the monthly charge goes up by $1.00 for every extra 10 pages. That has happened a couple of times and I am beginning to question the page counting. 100 pages a month is roughly 3 pages a day and I do not print anywhere near that number of pages. And I have the option to increase the monthly page allowance for just another dollar or two per month. TBD....
Bottom line being I am using OEM cartridges, thus far still saving money versus purchasing retail/big box store cartridges, and not putting the printer at risk for substandard or counterfeit ink cartridges.
Take a look at what, if anything, the printer manufacturer offers with respect to refill plans etc.. Just pay close attention to the fine print, and take a careful look at how much printing you anticipate by week or month. Plus keep some good records on how much you actually print.
The question of using third party inks, etc. may be rendered moot.