If I understand correctly your question you would like aeach sector of the brain to be able to execute two, or more, completelya different taskstype of task depending on the situation. We don't know if this is already happening, but a lot of observations have been made with tomography and pet scanners and it doesn't seem to be the case. Each group of neurons seem to be performing a very specialised task. If some areas of the brain appear to be active with many different types of reasoning chances are that they are performing low level tasks that are needed by many different higher level operations.
You may imagine a neuron as a component of a programmable logic device where the configuration is performed by altering chemically the sensitivity to a signal or by growing new synaptic connections. All the logic is built in the circuit. Each group of neurons can be configured into a circuit that performs a certain task, but it takes a while to reconfigure that circuit to perform another task, as it is the brain you imagine is unlikely.
A workaround could be a neuron that has a lot more synapses. The synapses could be working in groups, each active in a particular situation, thus there could be different circuits built around the same group of neurons. Trouble is, how to switch on or off a certain group of synapses? There could be an idea, a part of the neuron we understand little or nothing is the feedback synapse, it may suppress or enhance a signal, now we don't know when, how or why, but it would fit in your story as a group of switches that can quickly re-program some parts of the brain.
The drawback of such a brain is that the huge amount of synapses would increase dramatically the amount of heath to dissipate.