Is it permissible to collectively complete the Qur'an with neighbors in one house, where each person reads a portion?

The permissible and impermissible forms of gathering to recite the Qur'an have been previously explained in Fatwa no. 44983, which can be reviewed. If the khatmah you mentioned is the third form referred to in that fatwa, its ruling has already been stated. However, if you gather, and then each of you individually recites the portion she has chosen or been assigned, then in this case, none of you is considered to have truly completed the recitation of the entire Qur'an. Rather, the utmost that can be said is that it is a gathering and cooperation in doing good, which is a desirable and permissible matter.