The Talmud lays down the principle:
אֵין עוֹשִׂין מִצְוֹת חֲבִילוֹת חֲבִילוֹת -- One does not perform mitzvot in bundles. [Sotah 8a, also Pesachim 102b, Berakhot 49a]
Another Talmudic quote is intended to make this easy: One who is engaged in a commandment is exempt from performing another commandment. [Sukkah 25a]
Why not? Is this halacha? Is this fleshed out anywhere? We are taught in many other places that we are supposed to maximize the performance of mitzvot. So why not do several at the same time if it is feasible? Why assume it would just be rushing to get them out of the way? (You could argue that even with a single mitzvah.) The Talmudic principle "En mearvin simchah b'simcha -- Do not mix rejoicing and rejoicing" [Moed Katan 8b] is not relevant because we are not talking about joyous occasions.