nextgroup across line border

I want to create a syntax for filetype that looks like this:

item0onLine0 item1onLine1
item0onLine1 item1onLine1
separatorLine
item0onLine0 item1onLine0
item1onLine1 item1onLine1
...

In order to do this I try

syn match i0l0 /^item0onLine0/ nextgroup=i1l0
syn match i1l0 / item1onLine0\n/ contained nextgroup=i0l1
syn match i0l1 /item0onLine1/ contained nextgroup=i1l1
syn match i1l1 / item1onLIne1\n/ contained

, but this works on first line only. How can I have next group located on the
next line? `item0onLine1' cannot be matched reliably on its own. `item0onLine0'
is always matched reliably.