That's a bad idea for many reasons, and you know it.
Demo the old decking, and start fresh.
Don't buy big box store P/T lumber. It'll end up looking worse than your current Philippine mahogany (lauan) decking.
Try 5/4x6 knotty cedar...looks good, smells good, and is easy to work with. Maintain it, and it'll last a good while.

steve

I must agree with the other reply , you are asking for problems , is the substructure strong enough to support it? You will trap water which will cause mold, mahogany is a tight grain and will stain dark , it's the nature of the wood, have u tried to put a darker tone semi transparent stain on it? Seems like lots of money and time wasted just to replace so it so soon

Why are you hesitant to demo the existing decking? If you want to get it done for free, post on freecycle that you'll give the wood away to anyone who removes it. It'll be gone in a flash.

Thanks to everyone for your advice. I'm not at all surprised that everyone says the old deck should come off.

I'm not sure what we're going to do. We are planning on putting the house on the market, and I think it would help if the deck (actually a front porch) looked nicer than it does. The deck started looking bad almost as soon as it went in, about 5 years ago, and that's probably due to the crappy wood the person used (it's called Mahogany, but I know someone else with a real mahogany porch and our two porches look completely different from each other). On mine, the wood is cupping and the grain just isn't looking pretty (he put marine grade polyurethane on it when it was installed). The installer came back maybe two years ago and said he would sand and refinish it. Personally I was as unimpressed by his refinish job as I was with the initial install. It looked shinier, but otherwise no better.

So, I could leave it alone and hope it doesn't hurt the curb appeal too much. Or, I could sand and refinish the deck myself. If I do it I would remove a lot more material so I could sand the entire surface and not just the curved up edges of the boards (probably 1/16-1/8" of curl). Or, I could put new decking on (the structure underneath is fine, although I'd probably put plastic tarp on the ground). Unless knotty cedar is comparable in price to p/t, I'd probably go with p/t and maybe color it with Cabot stain.

And yes, I would remove the old wood. Probably with a sawzall, rather than a screwdriver.

No matter what I decide, I'll do the work myself, and try to spend as little money as possible. I've never installed a deck before but I'm pretty decent handyman (remember I said up front that I thought I knew what people were going to tell me about putting a deck over an older deck, and I was right. So don't let my initial question worry you too much). The whole thing is about 175 square feet (about 6.5x25 feet, plus two stairs, plus some trim on the vertical faces).

If I do this I'll probably post again because I have a few questions about what I should do in a couple of places. I would use a different pattern than the original guy did (straight runs of boards, instead of fancy mitered ends that now look terrible because the wood is shrinking and the miters are separating).

If anyone has other comments or suggestions they want to make, please do so. If not, thanks again for responding. I really appreciate it.

I would replace it still. Adding a new deck to your house will add more value than adding an additional bedroom. There are also plenty of material suppliers that are really pushing product right now so you might be able to get a discount. Look into getting a composite or something too. If not then look for a tropical hardwook like Ipe.

Now you say this is actually a front porch rather than a true deck. Is this a covered or open porch, can you post a few pictures? It may give us a better feel for the potential issues you may have as the two are generally handled differently from the type of materials used and the fasteners to hold them down.