Well, it has been done in 1959, by a French astronomer called Audouin
Dollfus (born 1924, still active). He went up to 14 000 meters, then a
world record, with a series of about 100 meteorological balloons, a
cluster 450 meters high. See pictures on this webpage (in French):http://www.astrofiles.net/article52.html- Hide quoted text -

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When I went to the website (reading in my limited french) I noticed
something very familiar to many glider pilots who fly in contests.
Notice the picture of Mr Dollfus speaking with microphones? (obviously
a seminar or convention) His laptop was covered with NASA, Flying,
Ballooning decals. I can't tell you how many other sufferers of
Icarus-itis, that I have seen with similar displays on their
equipment!
Micki