The claims of a patent define the scope of protection. Independent claims set forth (as the name implies) independent scopes of coverage, whereas dependent claims further limit (and thus specify a narrower scope of coverage of) one of the independent claims. US patent attorneys know that multiple dependent claims are generally to be avoided in the US due to the steep penalties (fee-based) imposed by the US Patent and Trademark Office. In contrast, many other jurisdictions, particularly Europe, broadly permit multiple dependency, and attorneys in those jurisdictions widely use them as a valuable tool.
Often this creates a mismatch when US-based applications are filed abroad, and vice versa. While there are various approaches to reconcile these situations, US-based applicants often miss the potential value provided by multiple dependency approaches. US practitioners often fail to realize that while such claims may be penalized in the US, there are still ways to use their concept in drafting US applications. This not only reduces issues when US-based applications are filed abroad, but it can actually help the prosecution applications in the US.
Consider the situation where a provisional application is filed first in the US. There are no restrictions to filing multiple dependent claims in a provisional application (as there is no requirement for any claim at all and no restrictions on claims). Therefore, the application can be drafted with many claims, including multiple dependent claim sets. Then, later-filed US and/or PCT and/or foreign applications can incorporate those initial claims as paragraphs in the specification and/or as actual claims if so permitted. The benefit of this is two-fold:
1) There will be literal support for any later-filed foreign application to utilize multiple dependent claims. Any foreign attorney working in a jurisdiction allowing such claims will gladly tell you how advantageous this can be both in terms of maintaining priority of your original filing date, and enabling desirable amendments during prosecution that keep the claims as broad as possible. For example, such an approach can reduce the "intermediate generalization" amendment problems in EP applications.
2) The disclosure of multiple dependent claims can count as original disclosure of a combination of elements that may not have been explicitly disclosed in the provisional application otherwise. For example, consider disclosure of two embodiments A and B, where feature C is further described with respect to embodiment B. A multilple dependent claim adding element C to two independent claims of A and B, respectively, may support a disclosure of the A+C combination.
When drafting an application that layers additional features and descriptions, the use of multilple dependency can further benefit the application.
It may be prudent when drafting a US provisional application to include multiple dependent claims. Further, when drafting a regular US application (or a provisional) it may also be prudent to include multiple dependent claims rewritten in paragraph form into the specification.