Yes, but ... .
You will probably get a reasonably good result from paralleling "dumb" drivers. Drivers which try to do 'clever' things in the way of protection or rise time etc MAY interact with each other in unexpected ways. Looking at the IC's or other drivers involved may be necessary.
That board appears to use 4 X A4983 microstepping driver ICs (Digikey $4.97/1)
At first glance these look "stackable" but there is enough "smarts" inside that a careful check should be made - or try it and see.
L6208 dual channel drivers rated at 5.6A are available
MC34921 about $10/1, appears at a glance to provide a full bridge tepper driver and 2 x PWM controlled DC motor drives in one IC,
DRV8829 (under $10/1) provides a 5A bridge in one pkg.
Stepper drivers usually use constant current drive to reduce rise times (t = L/R - constant current emulates a large drive resistance). Adding a small amount of series resistance from each driver and then commoning the resistors to drive the common stepper lead would aid load balancing. This should have little or no effect on the controller as the added resistances would be "seen" as part of the motor resistance and would simply be allowed for by the current source.
If you are happy to use 'dumb" drivers and do any logic work yourself you could use multiple driver ICs in parallel with very good results. An example are the rugged, cheapish and time honoured ULN2803 and family.
Each of 8 sections are rated at 500 mA continuous, so the package can drive 4A if all drivers are paralleled. In the DIP pkg shown here per driver dissipation max is 1 Watt and per package of 8 = 2.25 Watt - so care would be needed with dissipation. Use of external series resistors and sensible design would allow a 4 Amp driver with 4 of these IC's. About $US1 each in small volume.
Most flexible of all would be to use external driver transistors with a controller. A single TO220 device per channel (4 total) with appropriate heatsinking would allow in excess of 4A drive. I'd use MOSFETs but some may favour bipolars.