2 Payables Periods Pointing ot Same GL SOB - Can I open and close AP periods independently?

 I have 2 businesses that have their AP in separate Operating Units.  However, the 2 op units both point to the same SOB.  Is it possible to control the payables periods independently?  For example, one Op Unit needs to close Ap on business day (BD) 1 while the other needs to remain open until BD 4.

Is it possible to do this?  When I try in our test instance, it appears that Op Units pointing to the same SOB actually "share" the open/close status in AP...  Where the op units point to a different SOB, however, the opening and closing of AP appears to be independent.