Vinegar cannot be neutralized by adding water. Adding water to vinegar only results in a dilute solution of vinegar.
If vinegar were being neutralized by the addition of a base some of variables that could be controlled include the concentration of the vinegar solution. If an equal volume of two samples is being neutralized the sample that is more dilute will require a smaller amount of the base. The molar concentration of both the vinegar and the base should be kept constant. In addition the volume of the sample of vinegar used should be kept constant which would ensure the same amount of the base is required. The temperature of the setup could be kept constant by cooling it as neutralization results in the production of heat. The heat produced may alter the properties of the reagents.