At an older home, it is quite common to find multi-layer roofs, composition material over old comp or even over wood shingles (a real no no). Despite the popularity of shingling over a worn out roofing surface, the practice is marginal at best. In the photo below, the rust colored shingles are the old roof below.
The psychology of the consumer is such that clients tell me they plan to put yet another layer over a roof that already has two layers. And somewhere in folklore, they have been told that it is okay to have three layers.
There are many problems with the theory. For one, if you have ever carried roofing materials up a ladder, you know that it is heavy. You start adding too many layers of the stuff and you are putting way more weight on the roof structure than it was designed to carry.
Now that is one thick roof I am kneeling on. I wonder how much it weighs. Other problems include the shingles not sealing well, so they tend to blow off in wind in blustery Bellingham and Whatcom County; the shingles not lasting as long as the warranty would indicate they should. A multi-layer roof will have maybe 80 percent of the estimated design life. The extra thickness often puts the surface of the roof in direct contact with siding or trim at dormers and that promotes rot. Speaking aesthetics, such roofs look funny, all wavy and unattractive. That is part of the reason the shingles blow off -- wind can get under them.
It is my advice that, when the roof requires replacement, the old roof should be torn off and a new roof, including felts and flashings in most cases, should be installed.