More generally, (and more realistically), say we have 10000 variables but our computer only has enough memory to do regression with 6000 variables. (Having 10000 variables would not be unusual these days due to large datasets; additionally, some of the variables could cover seasonality and other easily observable factors.) Can we still run a regression controlling for all explanatory variables, despite our limited memory? Again, the answer is yes, due to the Frisch Waugh Lovell Theorem.
The video below uses R to illustrate how the Frisch Waugh Lovell theorem is used (a simple example is given on purpose, but it is easily generalizable).
Wonder how the Frisch Waugh Lovell theorem works? Well, here's the proof of the theorem.