I think which you might start in the primer design, improve the selection for most similar melting temperature and %GC among primers, avoiding dimer formation among them. After, could perform a single PCR to independent standardization next to multiplex PCR.
The next article is too old but it has some points to focus: Article Multiplex PCR: Critical Parameters and Step-by-Step Protocol
Multiplx PCR is different in a way due to the use of several primers. Meanwhile, your target DNA would be two or more. Therefore, you must use or select primers which will work in similar or closer Tm or annealing temperatures. Except those other parameters are same as conventional PCR. This paper might help https://www.ncbi.nlm.nih.gov/pmc/articles/PMC88949/