Most manufacturers allow shingling over another layer. Keep in mind most asphalt comp shingles will telegraph a pattern underneath, so the cupped shingles may prevent the roof from laying right. Personally, I always do a tear-off. Even though it is more work, it allows me to inspect the deck and install new felts and flashings. Given the fact, I won't come back for 20 years, I figure it is worth it. BUT it is not required. Get some zinc metal strips at the depot to prevent moss and mildew in the future. The zinc corrodes slowly (ZNO) and kills off the offending fungi.