There seem to be many widespread assumptions about helmet design, particularly regarding how well they handle multiple impacts. The poor availability of the relevant standards documents does not do much to help this.
As others have mentioned, relevant helmet standards include EN 1385 (for kayaks and whitewater sports) and EN 1077 (alpine skiers and snowboarders). There is some overlap between the standards, and it seems likely that the paucity of multi-rated helmets is more likely due to the expense of testing than significant design differences. Here is a rough comparison of the major requirements for these standards:
- Field of vision: (Both standards)
Making sure the helmet design does not interfere with the user’s field of vision.
- Extent of coverage: (Both standards)
Making sure the helmet covers all necessary parts of the head.
Shock Absorbing Capacity:
The most important is the shock absorbing capacity of the helmet. This is tested in a specialized instrument where the helmet is dropped:
- EN 1077: from 1.5m onto a solid metal anvil with a 4 kg metal head inside.
- EN 1385: with the speed of 2.5m/s onto a solid metal anvil with a 4 kg metal head inside.
Inside the metal head there’s an accelerometer that measures the forces within the impact.
- EN 1077: The helmets are tested in three conditions: Room temperature, -25°C, and after artificial aging.
- EN 1385: The helmets are tested in four conditions: High
temperatures (+35°C), low temperature (0°C), after artificial aging, and after the helmet has been submerged for 4 hours.
Each helmet is tested on several areas (crown, side, rear & front). The peak acceleration must not exceed 250G for any of the impacts.
Resistance to penetration: (EN 1077 only)
While skiing or snowboarding there’s a risk of poles, skis or branches penetrating the helmet. The resistance to penetration is tested by dropping a hammer with the mass of 3 kg from 75cm onto a sharp cone shaped metal punch placed against the helmet. The point of the metal punch must not reach the head inside the helmet.
- Bouyancy: (EN 1385 only)
After being submerged for at least 4 hours, the helmet must float to the surface.
- Retention system performance: (Both standards)
This test covers the strength of the retention system (webbing), as well as its effectiveness, i.e. the webbing's ability to keep the helmet securely positioned on the head.
- Durability: (Both standards)
After all these tests the helmet should not show any damage that would cause any additional damage to the wearer.
A helmet tested to the EN 1385 standard is not intended for use in white water class V and VI.
For those who haven't done the math, a 2.5m/s speed corresponds to only about a 0.3m drop, or about half the speed most helmets would be tested for. The reasoning is apparently due to the expectation that someone floating in water will have difficult reaching high speeds.
Beyond applying impacts to different parts of the helmets there is no multiple-impact testing included in the standards. Low-speed impacts to a helmet that meets either standard will simply fail to crush the foam and the force (though distributed by the helmet rather than focused) will be passed along to the head. (Some types of multi-impact helmets might make use of materials like EPP foam instead of EPS, but the rebound behavior of EEP is still, I believe, not yet well-characterized.)
 While the documents can be located, it is often required that they be purchased for prices far in excess of what the general public would be willing to pay. E.g. BSI sells a copy of the EN 1385:2012 standard for about $223 USD.