Let $S$ be a scheme and $\mathrm{Spec}(B) = V \subseteq S$ be an open affine. When using the affine communication lemma (c.f. Theorem 6.3.2, Vakil's notes, Foundations of Algebraic Geometry), one often encounters the situation 

$$
B = B_{f_1} \times_{B_{f_1f_2}} B_{f_2}
$$
(or its generalization with $n$ localizations, which I did not bother writing) because we get an open affine cover $V = \bigcup_{i=1}^n \mathcal D(f_i)$ by distinguished open sets. The usual trick to lift properties of the $B_{f_i}$'s to $B$ (finitely generated something-algebra/module, reducedness, noetherianness, etc) is to use this computation where we take high powers of the $f_i$'s and cancel them using the fact that $(f_1,\cdots,f_n) = B$. 

Question : is there any way to avoid these computations using some properties which lift correctly through the fiber product, or is this computation supposed to be there in each case? For instance, do any of the properties listed above satisfy something in the fashion "a finite limit of -*insert property here*- satisfies -*property*-"?

P.S. : Feel free to assume anything you want for the general statement I am looking for, as long as it involves doing this computation at most once.