This is an interesting thread to which I will bring a dose of oh god the boredom of regulation. You make a production gauge. When you do so you have to designate the product. Assume the production methods used meet the production procedures (19.77) you have on file for for bourbon, corn whiskey, and whiskey distilled from bourbon mash and also meet the the grain/proof standards (80% or more corn at not more than 160) for each. Once produced, you must immediately make a production gauge (19.304). The rules for production gauges state, "Spirits in each receiving tank will be gauged before any reduction in proof and both before and after each removal of spirits." (19.289). I read this to say that you can can have more than one removal of spirits ("each removal") from a receiving tank - or more than one receiving tank ("each receiving tank"). So, let's assume, in either case, three gauges, each of which is deemed a separate production gauge (19.304).
I see nothing that prohibits you from entering two of those to the storage account, where you put them into a stainless tank and cut them to 125 or less - this must be done after the production gauge (19.289), designating the first "bourbon designate" and the second "whiskey distilled from bourbon mash designate" (19.305). Then, you transfer (19.324) the first to new charred and the second to used oak as "bourbon" and "whiskey distilled from bourbon mash," respectively, and proceed through a nanosecond or more to create age. The spirits in the third gauge go directly to processing, where you bottle them as unaged corn whiskey.
I see nothing in the regulations that prohibit that and 19.304, 305, .324 and .289 seem to authorize it. At the least, it would be an interesting challenge to a TTB investigator or auditor who sought to challenge what you did. I think they would lose the argument that you violated any provision of the regulations. The caveat is that your records would have to include the gauge record (19.618 and 19.619) for each of the three production gauges, showing the quantity and designation in each case, and create the trail that would establish that the products are eligible for the designations you give them. Note that I have not mentioned a formula once, although someone's comment above that you have to have a formula for bourbon is correct, not to show what you did to it, but to show that you did nothing to it that would change the class and type under the special rules that apply to bourbon and not to other American type whiskeys. Now, the above discussions about the methods and procedures you use to create the spirits are a lot more interesting, but wasn't the original question :-).