Hi Brenda,
Of course as an architect who might be expanding a residence, the first choice is to remove the "old" aluminum siding and match what we are putting on the addition; however, as a low cost alternative, I have painted it with success. My recommendation to anyone is to visit their local paint store, such as Sherwin Williams and consult with them as to how to prepare the surface and what paint to use.
So, to answer your question, yes you can do it.
John
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John Lehman AIA
Lehman Associates, PC
Highland MD
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