Lang Partners, the same folks behind the Oleander apartments just five blocks down the road seem to be planning another building (or buildings). Not much else I know, but it appears they are hoping for 6 stories.
ZC-16-140 Real Estate 1001-1044 W. Rosedale NST4 to PD for 6 stories 08/10/16 09/13/16
UDC-16-18 Near Soutthside Located between S. Adams St., W. Rosedale St., College Ave, and Oleander Walk Owner/Agent: Lang Partners Requests a recommendation for approval for rezoning from NS-T4N to NST4
Here's the blocks mentioned, however I'm not sure the exact extent.
Because Lang owns the entire western block excluding the one house on the SE corner and most of the northern half of the eastern block, I suspect this could look like the Oleander project down the street where there are essentially two buildings. Checking tad, below is the land owned by Lang and/or "WASHINGTON ADAMS PROPERTY LLC" who I assume are an involved party.
Thats about all I know for know, but something to look out for to see what happens.