Coedition of a natural language text and its representation in some interlingual form seems the best and simplest way to share text revision across languages. For various reasons, UNL graphs are the best candidates in this context. We are developing a prototype where, in the simplest sharing scenario, naive users interact directly with the text in their language (L0), and indirectly with the associated graph. The modified graph is then sent to the UNL-L0 deconverter and the result shown. If is is satisfactory, the errors were probably due to the graph, not to the deconverter, and the graph is sent to deconverters in other languages. Versions in some other languages known by the user may be displayed, so that improvement sharing is visible and encouraging. As new versions are added with appropriate tags and attributes in the original multilingual document, nothing is ever lost, and cooperative working on a document is rendered feasible. On the internal side, liaisons are established between elements of the text and the graph by using broadly available resources such as a L0-English or better a L0-UNL dictionary, a morphosyntactic parser of L0, and a canonical graph2tree transformation. Establishing a "best" correspondence between the "UNL-tree+L0" and the "MS-L0 structure", a lattice, may be done using the dictionary and trying to align the tree and the selected trajectory with as few crossing liaisons as possible. A central goal of this research is to merge approaches from pivot MT, interactive MT, and multilingual text authoring.