Is the number of discontinuities unbounded?

[LFG List]

I am interested in knowing whether there are languages that allow a constituent
to be split up into an unbounded number of pieces.  For instance, a case
marking language that interleaved NPs in the following way:

	the-NOM the-ACC big-NOM little-ACC black-NOM white-ACC dog-NOM cat-ACC
chased.

	"The big black dog chased the little white cat."`

In this case the two NPs were split up into four pieces each.

Are there languages that allow constituents to be split up into three pieces?
four pieces? an unbounded number of pieces?

Thanks for any help.

Cheers,

John.