Consideration in committee of the whole
There is a precedent for the consideration of the disallowance of regulations in committee of the whole.  The circumstances were that a motion was moved for the disallowance of a series of regulations under the Defence Act, and it was considered that the advantages of the committee procedure of debate, where senators can speak more than once to a question, were more suited to the nature of the motion. In addition, each regulation could be considered seriatim. To be effective, any resolution of the committee of the whole would have to be adopted by the Senate, on report.