You're fighting deliberate design decisions by the manufacturer, so
it's a tough ask. There are projects online for replacing the
control electronics in particular models of inkjet printers.
Trouble is, besides needing a strong ability with electronics,
there's such an insane variety of different models that the odds of
finding a project matching your particular printer model are next
to nothing. Even going the other way and buying a used printer to
suit an existing project proved impossible for me (though mainly
because I'm in Australia, and this was many years ago).
One possibly more practical option might be if you can get the
cartirdges from a continuous ink system designed for your printer
model (again you've got the "SO MANY MODELS!" problem though). The
chips in them will have some way of being reset so the printer
thinks the cartridges are new again.
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