It's trivial to extend this format to support streaming. Here I imagine some specs for it.

Suggested BNF additions:

grammar ::= string-table ';' object-shape-table ';' ows value
streaming-grammar ::= string-table ';' object-shape-table ';' ows (value ';' ows)*

ows ::= *( %x20 / %x0A / %x0D )

Suggested specification phrasing:

The streaming format is recognized by finding a semicolon after the first complete JCOF value. Parsers not instructed to expect an object stream SHOULD recognize this situation and emit an error.

Implementations using the streaming grammar SHOULD emit a newline after the object shape table and after every emitted object (at the "ows" production in the BNF). This enables compatibility with existing line-streaming programming styles.