Detecting and quantifying extra virgin olive adulteration is of great importance to the olive oil industry. Many spectroscopic methods in conjunction with multivariate analysis have been used to solve these issues. However, successes to date are limited as calibration models are built to a specific set of geographical regions, growing seasons, cultivars, and oil extraction methods (the composite primary condition). Samples from new geographical regions, growing seasons, etc. (secondary conditions) are not always correctly predicted by the primary model due to different olive oil and/or adulterant compositions stemming from secondary conditions not matching the primary conditions. Three Tikhonov regularization (TR) variants are used in this paper to allow adulterant (sunflower oil) concentration predictions in samples from geographical regions not part of the original primary calibration domain. Of the three TR variants, ridge regression with an additional 2-norm penalty provides the smallest validation sample prediction errors. Although the paper reports on using TR for model updating to predict adulterant oil concentration, the methods should also be applicable to updating models distinguishing adulterated samples from pure extra virgin olive oil. Additionally, the approaches are general and can be used with other spectroscopic methods and adulterants as well as with other agriculture products.