Overblowing
How does one overblow? Do you need a special custom harmonica?
It helps to start on a harmonica that's as airtight as possible and gapped low. Something like a Discrete Comb (my product) or Suzuki Overdrive that lets you isolate a single reed can also help you develop the technique.
However, once you get a good feel for it you may find that you can get at least some overbends on a stock harmonica. Recently, while recording the CD for Blues Harmonica For Dummies, I used a stock, nailed-together Marine Band on one track that demonstrated overbends and was initially surprised that the 5 Overdraw came in pretty easily on that harp.
Custom harmonicas offer the advantage of being adjusted specifically to allow every possible overblow and overdraw to be dialed in and available instead of just the luck of how that harmonica came from the factory. Additionally, custom harps that are adjusted for overbends can offer greater ease at achieving overbends and even bending them up in pitch by one or more semitones, something you seldom find in a stock harmonica.
Stalling is the obvious problem - the lower you gap, the easier a reed will be overwhelmed by a low volume of air.
Some players put a dab of glue or wax or even adhesive tape on the reed near the base to help stabilize it against torsional vibration - the tendency of the reed to rock sideways instead of along its length that can cause it to squeal.
Also, you need to adjust both reeds for optimal response. When you use a blow breath to activate the draw reed that produces the overblow, you need to get the blow reed to stop vibrating. Gapping it low can help, but that can produce the stalling problem. Some customizers have a deep knowledge of how to do this well and can set up a harp to play easily at normal pressures, yet produce overblows that sound easily and bend up several semitones (Jason Ricci happens to be very good at this). Me, I'm just a trial-and-error tinkerer.
Tight embossing of the reed slot for more efficient air use and greater responsiveness is promoted by some players to make reeds overbend easier, while others say that good OB response can be achieved without embosssing and the bright tone it creates.
Check Kinya Pollard's reed adjustment videos - both the gapping videos and the sizing videos - here on bluesharmonica.com. You can also check out some more extreme procedures at overblow.com.
You don't NEED a custom harmonica, but it sure helps... at the very least setting your gap low helps. I don't teach overbending... subscribe to Howard Levy's site... that's his thing.