Personally, I would avoid it if possible. Even if they are of the same model, small discrepancies may cause their +12V to be slightly different. At the very least, will cause very non-uniform load distribution.
Luckily, seems the OP only needs one. The current light only uses 36W @ 12V, even if they make the new light 10x more powerful, a single 400W PSU should do the job nicely.
It's not like the fixtures consist of a single LED either. Should be trivial to parallelize.
What about wiring them in parallel with a voltage regular after.
Then you waste a ton of energy on the conversion and still have the same problem. You won't ever get two regulators at exactly the same voltage. One will always take most of the load.
You get around this with load balancing resistors, but that comes with its own set of problems.
The way you get around that is to chop up your load into multiple independent power domains. That way each segment is powered exclusively by one supply.
If you can't do that, you will always be better off with a single larger supply.
I meant in parallel so both positive terminals are connected to the regular in one node
Imagine one PSU outputs 12.0V another one 12.1V, and there’s no load whatsoever.
When you connect them in parallel, the first PSU should detect negative load i.e. actual voltage lather than the target; I have no idea how real-world devices handle that condition.
The second PSU will detect load i.e. actual voltage smaller than the target one, will probably assume it happens because the load is pulling energy and will try to extract more power form the AC source to compensate, to make the output stay at the +12.1V target.
I’m not an expert electronics engineer, but to me the approach looks like a recipe for disaster.
It’s usually fine to connect chemical batteries in parallel for two reasons. They have that discharge curve i.e. the voltage decreases monotonously while discharging. If one of them has slightly higher initial voltage, will discharge until matched with the other one, and then both will discharge at about the same rate. Also, chemical batteries have ~fixed internal resistance i.e. the more current you pull from one, the less voltage you get due to that internal resistance.
AC to DC power supplies don’t have a discharge curve because nothing to discharge, they continuously pull energy from the input AC. They don’t have the concept of internal resistance either: when more output current is pulled from them (i.e. the load increases), they simply increase input current from AC (to a point, and then either a fuse blows up or the device catches fire). The dependency between output current and output voltage is not necessarily monotonous. But the worst of it, it depends on time because capacitors, also because the input is single-phase AC i.e. at some moments of time the input power is zero because the input AC voltage and current are zero.