Multiple hyphens in a word

In ‘The Penguin Guide to Punctuation’, R L Trask identifies three cases in which a hyphen is required after a prefix. One of them is where a prefix is added to a word which already contains a hyphen. His examples are non-bribe-taking politicians, his pre-globe-trotting days, non-stress-timed languages and an un-re-elected politician.

In your example, self-sustaining is a word which already contains a hyphen and to which you wish to add the prefix semi-. The resulting semi-self-sustaining is consistent with Trask’s advice.

I don't personally think that using multiple hyphens is a general problem. I have often seen words like "four-year-old" and the like to make an example.

Since self-sustaining is written with a hyphen, I would go for semi-self-sustaining.

The Chicago Manual of Style, sixteenth edition (2010) glancingly affirms the advice that Barrie England cites from The Penguin Guide to Punctuation in his answer:

6.80 En dashes with compound adjectives. ...

A single word or prefix should be joined to a hyphenated compound by another hyphen rather than an en dash; if the result is awkward, reword.

non-English-speaking peoples

a two-thirds-full cup (or, better, a cup that is to-thirds full)

As Chicago very wisely observes, the critical question to ask in deciding whether to use multiple hyphens in a compound word is a highly subjective one: Does the result seem awkward? If it does, your best bet is to reword to avoid the awkwardness—not to press on in unthinking obedience to some set-in-stone rule about proper punctuation, regardless of the effect it has on the sentence you're trying to construct.