In engineering terms, it's possible, but to what end ? The real problem is a lack of a fast route between Leeds, Manchester and importantly for me, Sheffield - in my eyes, the only reasonable option is an entirely new line allowing very high speeds and vitally, missing out the intermediate Victorian era infrastructure limitations.
Where ? I'm not a betting man, but if I was, I'd take a direct line from the HS2 line south of Barnsley, directly into Manchester City centre in the straightest mostly tunnelled line, popping out west of Manchester and continuing onwards to Liverpool. It's a longer route, but isolation from classic rail allows for speeds of up to 250mph - route is about 90km, at an average of 200mph, would yield the target 30 minute point to point time between Leeds and Manchester, freeing up the existing line for more stoping services.