It depends, the second melt curve could be due to non-specific product or primer dimer or -in the case that the two melt curves are too close to each other- due to unequal GC distribution of your main product. Optimization of your reaction/cycling conditions or re-design of your primers could be the solution.
one can also do so called as a high resolution melting curve analysis. with that, we can get the exact melting temperature and definitely they will have different melting temperatures based on which you can further optimize your PCR reaction.
In my opinion, that means the primers are not specific enough so that they produce off-target products. I would not not wait and just re-design primers.
You can run gradient PCR around your primer TM and find the optimum temperature of your specific product with the lowest quantity of nonspecific band, and also add DMSO to PCR master mix also can be helpful to reduce primer dimer.