I had the same requirement, and found that Parameterized Trigger Plugin was not flexible enough for passing different parameters to different (or the same) jobs in parallel. Yes you can use a Parameter Factory with property files, but that would mean adding new property files to my version control solely for the purpose of configuring Jenkins. A Multi-Configuration project with a configuration matrix also seemed overcomplicated.
The better and more straightforward solution for me was the Multijob Plugin, which has the concept of Phases. A MultiJob can have multiple phases. Phases run sequentially and jobs within a phase will run concurrently (in parallel).
After installing the MultiJob plugin, when creating a new Jenkins item, select MultiJob Project. You can then create one or more phases.
Each job within a phase has it own parameters, click Advanced... -> Add Parameters
Also it is very easy to configure what should happen if a particular job fails, should the entire MultiJob continue or fail etc, see the Kill the phase on: and Continuation condition to next phase
when jobs' statuses are: settings.
For me this was much more intuitive to use than the Parameterized Trigger Plugin or a Mult-Configuration project, and did not require any extra configuration outside of Jenkins.