Alternate VP for William Henry Harrison?

If TR wouldn't do it to run in 1908, I doubt Mangum or any Whig would for that matter. He could, but it's not so likely and he'd be under pressure from his party to step down in favor of Clay.
I'm sorry, but could you clarify just a bit? Theodore Roosevelt served out the rest of what would have been McKinley's second term, and sought a full term in 1904. He declined to run for a second full term in 1908. As Harrison only serves about a month of his term IOTL and ITTL, any attempt by Mangum in 1844 will probably be seen as him seeking a second term, regardless of that not really being the case (just as with Roosevelt's "third term" in 1908). I think you're likely correct on Clay still running in 1844, Mangum was a supporter of his and would have deferred to him.
 
As Harrison only serves about a month of his term IOTL and ITTL, any attempt by Mangum in 1844 will probably be seen as him seeking a second term,

Whigs were opposed to Presidents serving two terms:

"Resolved, That these principles may be summed as comprising, a well-regulated currency; a tariff for revenue to defray the necessary expenses of the government, and discriminating with special reference to the protection of the domestic labor of the country; the distribution of the proceeds of the sales of the public lands; a single term for the presidency;"

That's the 1844 Whig Platform. If Mangum declares himself a candidate in 1844, many will argue that this contradicts Whig principles as he has already served one term. Whigs would already be mad at Mangum for assuming the Presidency itself and not becoming an Acting President instead, as they wanted Tyler to do. I think Clay might have enough support at the convention to overcome Mangum if the latter runs, look at Scott's victory over Fillmore in 1852.
 
Whigs were opposed to Presidents serving two terms:

"Resolved, That these principles may be summed as comprising, a well-regulated currency; a tariff for revenue to defray the necessary expenses of the government, and discriminating with special reference to the protection of the domestic labor of the country; the distribution of the proceeds of the sales of the public lands; a single term for the presidency;"

That's the 1844 Whig Platform. If Mangum declares himself a candidate in 1844, many will argue that this contradicts Whig principles as he has already served one term. Whigs would already be mad at Mangum for assuming the Presidency itself and not becoming an Acting President instead, as they wanted Tyler to do. I think Clay might have enough support at the convention to overcome Mangum if the latter runs, look at Scott's victory over Fillmore in 1852.
Mangum might actually become only "Acting President" ITTL, not sure what his opinion was on Tyler doing this IOTL.
 
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