How and when can solar charge controllers be stacked together?
In some cases it will be OK, in some cases you could expect significant problems. Knowing which is which is the trick. Here are some guidelines:

It will be seen that the answers are Yes, maybe and probably not, depending on the controller's capabilities. 

This depends on what the controller does. Having the circuit diagram (unlikely) or having someone reverse engineer the circuitry (easy usually) or observing behavior based on the guidelines below would help confidence in the result.

A solar charge controller should do some or all of the following. This list in approximate order of increasing complexity and reducing commonness and increasing price.


(a) ... Block back flow from battery to panel when panel voltage  is below battery voltage. This requires no more than a diode, but can be done wih eg Schottky diode (lower loss) or MOSFET switch (still lower loss, potentially).Could use a relay plus some sense circuitry but very unlikely. 
(b) ... Stop charging when battery voltage is "high enough".This can use a simple comparator and MOSFET switch or even just a relay. Relay's will be rare. When load is removed panel voltage will rise appreciably and battery voltage will drop somewhat, so a degree of hysteresis in measuring battery voltage set point is needed to prevent on/off oscillation. COULD be done by shorting panel output. Not usual but potentially viable. At say 10A from panel and 1 Volt across shorting system the losses are V x I = 10 Watts = easy enough to manage. 
(c) ... Provide a degree of battery management. Float / equalise / ... 
Battery university - excellent battery tutorial site -
(d) ... MPPT (MAximum power point tracking control) - steps panel voltage down to battery voltage in a way that holds the panel at its optimum power point for any given insolation (sunshine) level. A vast topic - but many MPPT controllers are available and a webs erach will turn up more than you want to know.  The suboptimal method (near MPPT) is mentioned below as it is liable to be of increasing commonness and of some relevance. 
Wikipedia on MPPT: 
Sub optimal "MPPT" method:


SO

Note below that when testing, if the PV source is limited to having Iout &lt;= Iinmax  for one controller then you are unlikely to do any damage.

(a) ... "Controllers" which are just  a blocking diode may be paralleled with some safety. They will tend to "current share" as if one diode takes more current its voltage drop will increase and this will divert more current to the other diode. Adding a small series resistor per diode will help current spreading but add (sligght) complexity.

Approximately R = 0.2/Imax ohms should help 

eg at 10 A R = 0.2 /10 = 0.02 Ohms. That's small!. Using separate wiring runs of a metre+ each in series with each controller would probably suffice.
Here at maximum current a controller see an extra 0.2V drop. Diode drop is about 1 Volt at full current so this is enough to imbalance flow towards a lower loss diode in a pair. More R has more effect.

Power loss is V x I so at 0.2 V and 10A P = 2 Watts. That should be bearable. Larger works better but wit more losses. 

(b) ... Low cost Asian no name controllers may use an over voltage switch and a blocking diode. The switch and diode may be combined in a single MOSFET. If these stop charging suddenly the panel voltage will rise suddenly and the battery voltage will drop somewhat. A second controller in parallel will see this potential drop in battery voltage as indicating that cutoff is not yet needed and keep charging slightly longer. I said 'potential drop" as it will keep charging and so reduce the effect of the disconnection of the first controller. For a short period the second (still charging) controller will tend to take double current.The period should be short and the controller will generally tolerate this - but not certainly. 

When charging is recommenced one controller will immediately increase the battery voltgae so the other will be less liable to then also start.

How all this inter-controller interaction works out depends on time constants, voltage decision levels, voltage hysteresis levels and over current ratings.

Best case two units with the same characteristics could share very well indeed. Adding a small resistance in the PV panel to controller lead may help. As above, this may just be longer than usual leads, depending on currents carried.

Worst case possibilities are 


Backwards and forwards handoff at boundaries. This is not necessarily bad but may upset customers.
One controller hogs the load and ultimately dies.


I'd say it was worth doing a real world test with two low cost controllers. here's a safe enough way to try it: Provide a PV source at about 1 x controller capability. Connect two controllers in parallel. Try with long and normal input leads. Observe results as battery reaches fully charged and as battery comes back onto charge. Using a small capacity battery will speed things up.

If you get no oscillation all is (probably) well. Oscillation may be OK as above. An ammeter in each controller wiring will show you balance but may affect results. If upstream resistance helps put ammeters there for testing. 

(c) As per b but interaction more likely. May not be serious as equalise is liable to be a low energy action. A single controller can probably happily equalise a much larger battery while the other controller sits there and sulks about the battery being over-voltage. 

(d) Probably not. Almost certainly. Two intelligent MPPT controllers with minds of their own are almost certainly going to fight. Even thesea re worth trying using a source limited to iin max for one controller.

The exception MAY be the suboptimal controllers that I mentioned above. There is an increasing tendency to do pretend MPPT where panel loaded voltage or output to input ratio is taken as a proxy for optimum power transfer. This may give close to ideal results. Often. Two such "MPPT" controllers may get on OK together as both have the same Vin target.