Can I put shingles on top of the old shingles without removing them?

Not if you want the shingles to do their job and keep your roof nice n' dry. If you don't pull up the old shingles (which I can only ume are deteriorating), the new ones can't make a proper seal to your roof, so rain water will seep under them frequently. I highly suggest you tear the old shingles out, or buy some buckets.