It can be done but is not optimum.
Old timers would break off the tabs on the old shingles.
No you don't paper over the old.
The best job is to strip, repair the roof decking as needed paper and
shingle.
There are even newer products than 15lb felt that will keep you
somewhat dry if a noreaster blows the shingles off.
wrote:
I have a three-tab asphalt shingle roof that I would like to re-roof
myself.
I've heard it is ok to just put asphalt shingles on top of the old (so
you don't have to scrape up all the old shingles) as long as it doesn't
go over three layers deep. Is this true? If so, should I be putting
down tar paper on top of the old shingles before laying the new layer?

Also, is there any disadvantage of going with fancier asphalt shingles
than three tab? I've seen some neat stuff from home depot
(manufacturer GAF) that look really neat, but are definitely not three
tab design.