My first preference would be to say no, but the committee could go with an option whereby all twenty-odd committee chairmanships would be voted on the same day and people could run for multiple committee chairmanships. If they were elected to multiple positions, they could resign from one and then have a byelection to fill the others.
We used to have that in the way we elected members of Parliament, such that members would actually get elected to more than one seat and then they would resign from one and choose the one that they wished to sit for. I think that would be problematic, but it's a possibility that the committee may want to consider.