No, don't change stuff once work has started.
Even if you can split it without changing the requirements it will change the way it is implemented because you will be effectively adding interface requirements between the sub tasks.
Ie.
Paint the fence red! Dev proceeds to buy paint sprayer
Paint this fence plank red. Dont change the colour of the pther planks! Dev throws away paint sprayer and scrubs paint off half the planks. Buys paint brush