[x] Make Houses exclusive communities with a strictly regulated number of members, based on the number of "points" that House has earned. Enforce the rules on assigning the points on a standard qualifying system with a rigid number each teacher/Prefect can add/remove in any timeframe. All changes in points are not only shown publicly, but have a (brief) description of reasons posted alongside it where every student can learn of it. Winners at House competition receive special treatment in a manner that doesn't infringe on the learning process (some superficial stuff like their colors prevailing in decoration of Castle, or the food choice of a day decided by the House voting, etc.). Entering a House is a special, but not necessary public ceremony which can be allowed to any student of Hogwarts from the 3rd Year and onwards. Each House may have their own criteria for membership. All members of any House have mandatory standards of acceptable grades and behavior. On a special occasion a member of Faculty or a majority vote of the House may exile a member who breached the conduct/school rules in a severe manner. The slot of the exiled member cannot be filled until the end of the Year to underline the importance of such decision. The Headmaster has a right of absolute authority in these matters, in exchange for the expected unbiased judgment. Any matters of conflict, like bias among teachers, the lack of commitment of school resourses towards the House privileges, unfair exiles initiated by Faculty, etc. - can be addressed to the Council of Directors by the student body. There may or may not be Student self - organization structure, i.e. Prefects (starting from Year 3), but it all depends on the number of students attending.
Um. Well, I just like the idea of Houses? I admit that I skimmed the organization of Durmstrang, so I remember almost nothing of it; not sure how much of it is similar.