The Weekly Shtikle - Tazria/Metzora
The first source that must be considered is an incident in Navi which is, in fact, the haftarah for Parshas Metzora which we will not be reading this year. In Melachim II 7:3 we are told that there were four metzoraim at the gateway. In the events that ensue it is clear that these men were together. However, this may not be brought as a proof one way or the other for a number of reasons. First, Chaza"l tell us that these four men were Geichazi and his sons. In the sefer Nachalas Shimon (by Rabbi Shimon Krasner of Ner Yisroel) it is pointed out that if a metzora would require absolute solitary confinement it would be because it follows the laws of "nidui," excommunication, in which no one may be within four amos of the "menudeh." However, in the Shulchan Aruch (YD 3l4:2) it is stated clearly that even one who is in nidui may be with his kids. Additionally, many commentaries point out that this particular instance of tzora'as is anomalous in that it was the result of a curse from Elisha that the tzora'as of Na'aman (see this week's haftarah) should inflict Geichazi and his sons.
Rashi on the words "badad yeisheiv" writes that "other 'temai'im' should not dwell with him." This might seem to indicate that he does in fact require solitary confinement. However, Rashi's intent is made more clear in his commentary on the gemara in Pesachim which Rashi is quoting here. There it is clear that the meaning is that other "types" of temai'im such as zav and tamei meis may not dwell with the metzora but it would seem that other metzoraim are allowed to dwell with him.
Nachalas Shimon on Melachim II deals with this issue at length and the conclusion is that it seems to be permissible. Tzafnas Pane'ach, as well, reaches the conclusion that it is allowed. Malbim here also writes that a metzora may dwell with other metzoraim and he fits into the precise definition of the word "badad," that it implies a separation but not an absolute confinement for we see the word badad referring to an entire nation at once (Bemidbar 23:9).
Nevertheless, the sefer Minchah Belulah writes that metzoraim may not dwell with each other for they are not equals.
Have a good Shabbos and Chodesh Tov!