In most cases the simple answer is "no, not economically. Buy a .44 Magnum, it will be cheaper."
Most important reason is the frame of most all .44 Specials can not handle the increased pressure of .44 Magnum. It's something like 14,000 psi vs 38,000 psi or double the pressure must be withstood.
The only thing I can think of that might come in .44 Special that could handle the pressure is a Ruger single action. Some old, some new, all are rare and you would be crushing it's collector's value at a cost of $300 to $1000 to you. You could find someone to trade guns with you even-up, costing you nothing.
Why change? .44 Special is far cooler then .44 Magnum!