The answer depends on what you mean by “proper,” as we will explain.
The gemara[1] does discuss having more than one ba’al korei for the reading of Megillat Esther, but this refers to their reading the same p’sukim out loud at the same time. Such a reading is valid,[2] although rarely done. The Magen Avraham[3] is the first major posek to discuss dividing the Megilla by sections, in a case of a ba’al korei who loses his voice in the middle of the reading.
Since the question is not discussed in the gemara or Rishonim, early Acharonim looked to parallel areas of Halacha to resolve the question. The Magen Avraham compares this situation to one in which the person reading the haftara had to stop in the middle of the reading, in which case the replacement must return to the beginning of the haftara[4] and repeat the beracha.[5] The Magen Avraham writes that in the case of Megillat Esther as well, the second ba’al korei should return to the beginning of the Megilla, but he does not recite any beracha again, because the first ba’al korei’s berachot were said on behalf of everyone. We find a similar ruling regarding a switch in the shofar blower; one who takes over as the second blower does not repeat a beracha.[6] Indeed, the Rama[7] rules that one is allowed, even l’chatchila, to make the beracha on the Megilla reading for the reading of another person.
The great majority of Acharonim disagree with the Magen Avraham and posit that the second reader does not need to return to the beginning of the Megilla.[8] The Eliya Rabba[9] and Shvut Yaakov[10] agree with the comparison to shofar blowing, but apply it more completely. Thus, they maintain that just as regarding shofar, the first blower’s blasts need not be repeated,[11] the subsequent ba’al korei for Megillat Esther similarly does not need to repeat the p’sukim of the Megilla that were already read. This differs from a situation in which a second ba’al korei takes over in the middle of a regular Torah reading, in which case the reading must be repeated from the beginning.[12] That is because the entire reading must be linked to the opening and ending berachot of the oleh; it is therefore problematic when the first oleh recited only the opening beracha and the second recited only the concluding beracha.[13] The Eliya Rabba[14] says that Megillat Esther is different in that the concluding beracha is not strictly related to the reading. Furthermore, while the beracha for Torah reading is made by the oleh for himself, the beracha for Megillat Esther is made on behalf of everyone. Therefore, anyone may continue reading Megillat Esther where the first reader left off, based on his beracha. The Shvut Yaakov writes that the first reason of the Eliya Rabba is not universally accepted, but he agrees fully with the second one.
It would seem that according to the Magen Avraham, breaking up the Megilla among different ba’alei kri’ah is quite problematic, since the later ba’alei kri’ah do not go back to the beginning of the Megilla.[15] According to the authorities who rule that the second ba’al korei does not need to repeat the reading from the beginning of the Megilla, is it proper to divide the reading l’chatchila? The cases that the poskim discuss are situations of a ba’al korei losing his voice; this might indicate that we would not otherwise allow the division. Alternatively, one might argue that it was simply not common practice to divide the reading, and no halacha precludes the division even l’chatchila. The Shvut Yaakov writes that the reason we do not return to the beginning of the Megilla, at least as a stringency, is due to tircha d’tzibbura;[16] this might imply that were it not for tircha d’tzibbura, stringency would be appropriate. Furthermore, some poskim who cite and accept the Shvut Yaakov’s opinion[17] recommend that if the community does not care about the extra time or if only a few p’sukim were already read, the ba’al korei should return to the beginning. This indicates that many poskim do not view the set-up we are discussing as l’chatchila.[18]
Thus, a “purist” minyan should not agree to divide the Megilla reading. First, it makes sense to defer to the opinions of the Magen Avraham (who apparently requires going back to the beginning of the Megilla) and of others (who maintain that one should preferably go back). Second, it is probably also more respectful of the mitzva to have one person read the whole Megilla, as we do in the case of many other mitzvot. In addition, due to the prominence of the mitzva of reading Megillat Esther, it makes sense to have the best available ba’al korei read everything.
However, not all situations lend themselves to purist approaches. There are many places where it is difficult for anyone to learn the entire Megilla well, and there are many communities in which the importance of involving as many people as possible (especially the community’s youth) is part of the shul’s or the educational institution’s very mission.[19] This is a local rabbi’s call. (Note that given that the well-known division into ten-chapter is non-Jewish in origin, it is somewhat distasteful to break up the reading exactly in that way.)