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I think you misread the datasheet - 500 mA. The datasheet says per driver but then all the current goes through the single ground pin so I suspect 8*500 would kill it.
The chip limit is defined by the thermal characteristics which are dependent on current, voltage drop, ambient temp and chip type (dip or soic). You have to add up the wattage dissipated by each driver and then multiply that by the thermal resistance of the package (from the datasheet). Add to that the ambient temperature and if its above 150C, it's a problem. I'd try to keep the temp below 100C, though. don't forget to factor in duty cycle, by the way.
an example: I think the voltage drop of the driver is .7V so at 500mA, the one driver would dissipate .35W. If it is a DIP package, the thermal resistance is 70C/W so 70*.35 is 24.5C. Add that to 25C ambient temp and you get 49.5C, well under the the limit. However if you have 3 drivers at 500 mA, we are looking at 98.5C - pretty hot but still within spec. If you use a SOIC, its a lot worse - 120 C/W - 42C per driver. For 3 drivers at 500 you get 151C - magic smoke time.
Note, I'm just guessing at the voltage drop.
edit: I just noticed in the ST datasheet there are 2 charts that will help you figure it out. Fig 10 and Fig. 11 are fairly easy to read though they presume a very high ambient (70C).