Cellular regulatory networks are organized such that many proteins have few interactions, whereas a few proteins have many. These densely connected protein "hubs" are critical for the system-wide behavior of cells, and the capability of selectively perturbing a subset of interactions at these hubs is invaluable in deciphering and manipulating regulatory mechanisms. SELEX-generated RNA aptamers are proving to be highly effective reagents for inhibiting targeted proteins, but conventional methods generate one or several aptamer clones that usually bind to a single target site most preferred by a nucleic acid ligand. We advance a generalized scheme for isolating aptamers to multiple sites on a target molecule by reducing the ability of the preferred site to select its cognate aptamer. We demonstrate the use of this scheme by generating aptamers directed to discrete functional surfaces of the yeast TATA-binding protein (TBP). Previously we selected "class 1" RNA aptamers that interfere with the TBP's binding to TATA-DNA. By masking TBP with TATA-DNA or an unamplifiable class 1 aptamer, we isolated a new aptamer class, "class 2," that can bind a TBP.DNA complex and is in competition with binding another general transcription factor, TFIIA. Moreover, we show that both of these aptamers inhibit RNA polymerase II-dependent transcription, but analysis of template-bound factors shows they do so in mechanistically distinct and unexpected ways that can be attributed to binding either the DNA or TFIIA recognition sites. These results should spur innovative approaches to modulating other highly connected regulatory proteins.