ZydoSEO makes a good point - I was assuming a like-for-like redirect (i.e. the same content on a new name).
If you're redirecting to different content, each redirect will be evaluated on a case-by-case basis, as ZydoSEO implies. You would then lose value in each instance where Google did not believe the content was a good enough match. You may also be subject to additional filtering intended to avoid direct transfer of value for domain purchases and similar, although the key factor is the content.