Many small- to medium-size table saws have relatively short arbors that do not safely accommodate a full stacked dado blade set. This isn't a problem when using a single saw blade, but when trying to use a 3/4-inch stacked dado blade, there isn't enough thread to allow the nut to be safely threaded onto the arbor. While there's no way to extend an arbor to make it longer, and it can be very unsafe to try to use a dado blade that doesn't fit, there are a few possible solutions to this problem.
Arbors May Be Short for a Reason
A short arbor on a saw is usually there by design, and it often relates to the motor power. A table saw (or radial arm saw) must have a strong motor to handle a deep cut with a full dado set without the motor bogging down under the load. If the motor's rpm drop too far, the chance of kickback increases.
Don't Skip the Washers
Out of desperation, you may be inclined to attempt to use a dado set without the arbor flange (on the motor side of the blade) or without the arbor washer (on the nut side of the blade) to fit in more chippers in your set. This is a very dangerous setup, as the arbor washer and flange are needed to help stabilize the blade. You should never use your saw without both the arbor washer and arbor flange properly installed.
You should also never install so many chippers that the arbor nut is not fully threaded when tightened. In other words, make sure that the arbor fully extends through the arbor nut. If you cannot see that the end of the arbor extends at least minimally past the arbor nut, then the nut isn't fully installed and presents a potentially dangerous situation. Instead, remove a chipper or two and re-attach the outer dado blade, arbor washer, and nut.
Try Blade Stabilizers
Blade stabilizers are large, washer-like discs that help prevent vibration and minimize runout when using single blades. They can also be used with dado blades. While stabilizers have a larger diameter than arbor washers, sometimes they are also thinner. If so, you can replace an arbor washer (on the nut side) with a thinner blade stabilizer to pick up a bit more room for the dado blade.
If the arbor flange is not fixed to the arbor, you also have the option of replacing it with a stabilizer on the inside of the blade. With thinner blades, it is standard to use stabilizers along with arbor washers and flanges, so that the stabilizer is against the blade on both sides.
Another Way to Cut That Dado
A table saw with a short arbor may be able to accommodate just the two outer blades of a dado set, along with a chipper or two, giving you a 3/8-inch-wide to 1/2-inch-wide cut. But this doesn't mean you're limited to 1/2-inch dadoes. An easy solution is to make two passes. Simply align the fence and cut one side of the dado (or rabbet), then adjust the fence and make a second cut to complete the dado at full width. While it takes a bit longer to make the dado, it is less taxing on your saw's motor and much, much safer than using an improperly installed dado blade.