tempera grassa

The concept that you mention comes out of the beginning of the 20th century when many painting technique researchers were obsessed with the idea that the Old Masters regularly used artificial emulsions (eg egg and oil, gum and oil) as their paint medium or alternated between those and straight oil paint or varnish. Max Doerner was a big proponent of this and the interlayering of soft resins. Almost all of this has been completely debunked by subsequent analysis. There was a recent conference at the Doerner Institute that focused on this. Kristin and I both presented at this conference.
As to whether one can paint fatty tempera over oil layers. The answer would really depend on many factors, including the proportion of oil, drying time between layer, etc. The short answer is it is not a good idea. There are many, many examples of works created during this period that have real structural problems including delamination of interlayers. In fact, the Doerner has many samples of works created during the heyday of this movement including works and samples created by researchers and students and many of these have fared poorly over the years. I know that there are some proponent of this working method but there is little to no evidence that it was practiced by the Old Maters, at least those works that have survived long enough for them to be examined using current methodologies and analytical tools.