Assuming a takeoff alternate was filed, couldn't you immediately head in that direction, declare an emergency, talk to ATC and/or company to determine feasability of other nearby airports? Dispatch should be able to give you performance numbers and weather for airports along the path towards the T/O alternate. Should one look at or above minimums and have the required performance, put the airplane on the ground. Hopefully ATC or company has rolled the trucks out to meet you.

Would this be a potentially good move? In the absense of any information, head to the alternate. Then as more info is gained (and assuming it is determined that an ASAP landing is needed) from your resources, company and ATC, make a decision to try a non filed airport assuming wx and performance are good.