Can I control multiple stepper motor drivers from one controller?
Utilizing six motor drivers for six motors is nothing unusual. As long as your controller output pins have a fanout of greater than six, you will be fine. This means that one output pin can drive six or more input pins of other ICs. If the fanout is lower (unlikely in my opinion), just use a buffer IC (e.g. 7406) to increase the fanout.

The alternative is, as Dave Tweed has already suggested, to use less drivers and hook up some or all motors in parallel. Obviously you should make sure the driver is capable of delivering the current. Further, only use identical motors in that setup, and don't use smoother steps than the proposed 1/4. The finer your microsteps become, the higher the probability that they will get out of sync. Also note that if one motor stalls, the other ones have less torque. If five stall, the last one might have to little torque left to even make a step. This will require balancing between motor type, driver, and how many motors per driver. You'll also want to use "dumb" drivers, like the DRV8812, which don't provide stall detection and tricky feedback-dependent things.

I personally don't recommend the last option. One fat driver can come close in price to six smaller drivers, so the saving won't be too impressive.

In both situations, care must be taken if the stepper shafts are connected mechanically. Even within one stepper series, you will get 5% step inaccuracy, leading to higher current drain than when not coupled and idle. They basically tug on each other because they don't perfectly agree on where the step center is.

I'm just thinking about whether it might be better to hook the steppers up in series (per-coil). Since most stepper drivers use current sources, that should allow the steppers to hold lockstep even for smoother microsteps. And it would solve the reduced torque problem when some motors stall. You'll need higher voltage rating for the driver then.