Can I insert an adjusting period into a calendar that is in use?

We are considering inserting an adjusting period into our GL calendar.  We want to use this period to close out our income statement and revalue our assets as a result of an acquisition and record any entries associated with the aquisition.  The thought is that this will allow us to report through May as Company A and from June forward as Company B.

We are on a calendar year.  We want to create an adjusting period between May and June.  May is currently our period 5 and June is our period 6.  The June period has not yet been opened.  

Can we insert an adjusting period and make it the sixth period and increment the June and subsequent periods by 1?  We do not intend to change anything else about the GL periods, their naming convention, date ranges and so forth would be the same. The only difference would be the period numbering and there would be an adjusting period with an overlapping date range (June 1 to June 1).