Tosefta zu Divrej Hajamim II 29:37

All may enter to build, or to repair, or to remove any impurity. [Where there is] a commandment [that it is incumbent upon] Priests [to perform], [if] there are no Priests, Levites may enter [to perform it], [and if] there are no Levites, Israelites may enter [to perform it]. [Where there is] a commandment [that it is incumbent upon] those in a state of purity [to perform], [if] there is no one in a state of purity, impure people may enter [to perform it]. [Where there is] a commandment [that it is incumbent upon] those without a blemish [to perform], [if] there is no one without a blemish, those with a blemish may enter [to perform it]. [Where there is] a commandment [that requires one to enter Holy portions of the Temple] inside crates [so as not to gaze at the Holy, see Middot 4:5], if there are no crates, they may enter [by walking] through the doorway, and thus it says (2 Chron. 29:16): "And the Priests entered the House of the Lord to purify it, and they took out all the impure things, [etc.]." Rabbi Yehuda says, the storage areas that are under the Holy possess no sanctity, but there is sanctity in the roof ("ובגנו" not "ובגגו") of the Holy, [and] they do not eat holy offerings there, and they do not conduct sacrifices of lesser sanctity [there], but impure people that enter there, behold, they are exempt.