Provided are processes for making, and processes for using triglycerides as plasticizers. The process for making the triglyceride plasticizer includes: (i) recovering at least one linear C4 to C10 aldehyde, one branched C4 to C10 aldehyde, or a combination thereof from a hydroformylation product; (ii) oxidizing the linear, branched or combination thereof C4 to C10 aldehyde to form a linear, branched or combination thereof C4 to C10 acid; (iii) esterifying the linear, branched or combination thereof C4 to C10 acid with a polyol to yield a linear alkyl triglyceride, a branched alkyl triglyceride, or a combination thereof, and reaction byproducts; (iv) purifying the linear, branched or combination thereof alkyl triglyceride to form a plasticizer stream, a reaction byproduct stream, and an unreacted input stream, wherein the total carbon number of the triester groups ranges from 20 to 25 for greater than or equal to 45 wt % of the plasticizer; and (v) recycling from the purifying step back to the esterifying step the unreacted input stream and the reaction byproduct stream.