[CentOS] ssh & ksh question

I need to run a report, source file on system 1, on system 2. I'd like to
do this in one script, not have a second script to run it.

Now
cat script | ssh system2
works fine. But no matter what I've tried, it gags on
ssh system2 <<EOF
blah, blah
EOF.

Mostly, I have a multiline awk script in the script, with \ at the end of
each line... *but* I think it's seeing "\n" as an eol, and complaining, of
course.

Suggestions?

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