Two or more Diac Triac dimmers in parallel
Parallel connection of 2-wire dimmer switches is fine. 

Note that the first one to switch on will control the brightness. i.e., The one with the brightest setting will win. This is due to the way the triacs in the dimmers switch on at a certain point in the mains cycle.



Figure 1. Triac dimmer control. Note that the earlier in the mains cycle that the power is switched on the brighter the lamps. 


  I do not have a problem if the brightest one wins. I just want to know whether they will create a short or explode or destroy the load.


No, there will not be a short. The first one to switch on will drop the voltage across the other dimmers close to zero and the C1 on each of those will not charge any further and those triacs will not turn on.



The question changed somewhat after I wrote the answer in that OP can accept a "one triac" solution.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. A relay controlled dimmer with three preset power levels.

Figure 2 shows how to wire the dimmer for three-point relay control. The 4k7 resistor can be omitted provided the other resistors are greater than 4k7. I have laid the circuit out with the triac on the live wire as would normally be the case in a fixed installation. It will work either way.