Which chip to control four 3-digit 7-segment LEDs?

I'm creating some digital gauges, and want to use 3-digit 7-seg LEDs to display readings from four different sensors.

I've got one 3-digit LED working using two 74HC595 shift registers, but obviously this isn't ideal due to the amount of current they can sink, so I'm looking for alternatives. Other shift registers, like the TCP6B595N, still require 7 arduino pins for 3 digits, so I'd need 28 pins in total... a lot.

I know the MAX7219 can control up to 8digits, but does it treat those as one chained LED, or could it control three separate LED blocks at once? Or do I just need four MAX7219 chips; one for each 3-digit block?

Are there any other chips worth looking at?

Yes, you can use four discrete common cathode digits with the MAX7219. They will have their segment pins wired in parallel (As, Bs, etc) and each will have a unique common anode pin. ('digit' output from the MAX7219).
You can have each MAX7219 drive two 3-digit displays if that is what you are asking, for 12 digits total.

Yes, that's the summary I needed: two MAX7219 to run 12 digits.

I'll leave this open in case anyone wants to volunteer other chips as well.

Ht16k33. One chip/module could run all 4 of your 3 digit displays. 2 Arduino pins needed.

In fact, each module can run up to 16 digits and up to 8 modules can be connected to the same 2 Arduino pins.

Less than £1.50 on eBay.

That is a handy looking multiplexed module Paul, and it is so nice to see a Holtek chip again. ( it fits in with the other bit of good news about the Arduino companies being reunited )

Before I discovered Arduino, I had been designing with CMOS logic chips, and any remote control requirements always used the HT12 series Holtek chips. ( Circa 1983 )

Thanks Paul. I've ordered one of those boards to try out ($1.60 from China), so we'll see how it goes.