...so too do I regret..... This is the correct form.

Fiona, In spoken language, instead of using inversion, we often use stress or some other way of phrasing. Mandatory inversions are mostly for grammar tests and very fomal writing. Examples: Never have I seen a car like that....(With inversion it sounds very stiff and formal.) I have never seen a car like that....(The normal way of saying this.) In your sentence the inversion is used to emphasize the positive agreement of the second clause with the first. Just as Oppenheimer came to regret his contributions to the first atomic bomb, so too do I regret my participation in what was, at the very least,an error in judgment. When speaking you can get the same emphasis by stressing the pronoun "I". And we are talking about the spoken language in your quote. Just as Oppenheimer came to regret his contributions to the first atomic bomb, so too "I" regret my participation in what was, at the very least,an error in judgment. ------- Concerning whether it is grammatically correct...the only place you will ever have to worry about that is on an ESL grammar test. Here are some examples of written versions of "so too" without inversion: -For if it occurred to me that I might occasionally excite suspicion by the little outbreaks of my sharper passion for them, so too I remember wondering if I mightn't see a queerness in the traceable increase of their own demonstrations. -From The Turn of the Screw by Henry James Just as he liked and praised a country life in comparison with the life he did not like, so too he liked the peasantry in contradistinction to the class of men he did not like, and so too he knew the peasantry as something distinct from and opposed to men generally. -From a translation of Anna Karenina byTolstoy. For the things we have to learn before we can do them, we learn by doing them, e.g. men become builders by building and lyreplayers by playing the lyre; so too we become just by doing just acts, temperate by doing temperate acts, brave by doing brave acts. -From a translation of The Nicomachean Ethics by Aristotle I would say that your instincts are correct. Inversion is not always mandatory after "so too".

Just as you are as you are anxious about tomorrow's meeting, so too am I. Just as Shakespeare was a poet and dramatist so too was Ben Jonson though not as widely read.