[Shen & Joshi, 2005] use the term 'semi-incremental' to refer to parsers (both left-corner [Collins & Roark, 2004] and head-corner [Yamada & Matsumoto, 2003]) which permit multiple iterations of left-to-right scans, rather than just one.
to these models, [Shen & Joshi, 2005] introduce an approach for incremental parsing of spinal Lexicalized Tree Adjoining Grammar, which supports full adjunction, a dynamic treatment of coordination, as well as non-projective dependencies.