paraffin is aliphatic hydrocarbon chains of varying length. The longer the chain the higher the melting point and the same goes for branching. Shorter chains could be added but i question whether they will be separated as the temperature decreases and the block sets..
Thee best solution is to select a grade which already exhibits lower melting point. Mixing of waxes with different melting points or with other low molecular materials also reduces melting point (eutectic). There is an huge selection of waxes with various metlng points.
It would be good to know why you want to reduce the melting temperature of paraffin. Maybe there are other ways to accomplish whatever you are trying to do.
Any oily additive you added can reduce the hardness (increase penetration test mm / 10), if the hardness is an important parameter for you. I suggest you look for the macrocrystalline paraffin with the lowest possible congealing point and mix until desired value. One possibility is to add stearic or palmitic acid. They are likely to maintain the hardness and lower the freezing point.
Yes, you can. In fact, paraffin waxes with low melting points are manufactured. They just aren't called "paraffin wax." For example, paraffin wax with a melting point close to human body temperature is commonly called "petroleum jelly" or "Vaseline." Different name but essentially the same thing, mixed hydrocarbon chain molecules. The shorter the range of lengths, the lower the melting point. Paraffin wax with a melting point below room temperature is called "mineral oil." By mixing (melted) paraffin wax with either of these two substances (petroleum jelly or mineral oil) you would create a paraffin wax with a lower melting point.
Further, you can pick up nonadecane to hexadecane to get 32-18degreeC melting point. Also you can add some impurity to disturb crystallization and the melting point will decrease.
Melting temperature of PCM ranges between 18 to 60 C. One can reduce the melting temperature by adding inorganic salts (PCMs), which is called as eutectic PCM.
You may want to check also the following somewhat related RG discussions: https://www.researchgate.net/post/Where_are_the_melting_points_and_viscosities_of_waxes_tabulated2