An integrated circuit may include programmable logic regions coupled in parallel to an interconnect bus. Multiplexing circuitry may be interposed between the programmable logic regions and the interconnect bus. The multiplexing circuitry may be formed from multiplexing circuits formed in a cascade structure. The multiplexing circuitry may dynamically receive control signals that determines which programmable logic region is allowed to drive output signals onto the interconnect bus. Alternatively, each programmable logic region may have an associated output circuit that is coupled to the interconnect bus. The output circuits may be dynamically controlled by control circuitry. The output circuits may receive control signals from the control circuitry that selectively enable and selectively disable the output circuits. The output circuits may be formed with logic circuitry that ensures that the interconnect bus is not simultaneously driven by the output circuits.