Short Answer
Sometimes. Whether it is permitted or advisable depends on the specific roof, existing layers, code, manufacturer requirements and substrate condition.
Detailed Explanation
Installing new shingles over existing shingles (called a 're-roof' or 'overlay') is sometimes permitted and can save on tear-off and disposal costs. However, it's only appropriate under specific conditions: there must be only one existing layer (codes typically allow a maximum of two layers total), the existing roof must be in good condition (no widespread damage, no curling or buckling), the deck must be sound (which can't be fully verified without tear-off), and the manufacturer must allow installation over existing roofing for warranty compliance. A re-roof doesn't allow inspection of the deck, doesn't allow replacement of deteriorated flashing, and adds weight to the roof structure. In most cases, a full tear-off is the better long-term investment because it ensures the new roof is installed on a properly inspected and prepared surface.
Why It Matters
Re-roofing may save money short-term but can hide problems, add weight, and compromise warranty coverage. A full tear-off is usually the better investment.
When Repair Makes Sense
Existing roof has only one layer, is in excellent condition, and manufacturer allows overlay.
When Replacement Makes Sense
Existing roof has damage, multiple layers, or the deck needs inspection — full tear-off is required.