We are interested in developing a computational architecture to support the dynamic creation of multilevel representations in the design and implementation of complex systems, including physical artefacts, social systems, and socio-technical systems. This is motivated by a longer term goal of understanding how to model autonomous evolving multilevel systems, e.g. to create self-programming computer systems, or to model and forecast the evolving dynamics of multilevel narratives in social media. Design is the process of taking sets of parts at one level of representation and assembling them into wholes with emergent properties at a higher level of representation. It is common for an assembled whole to become part of a whole at an even higher level. In the first instance the parts, intermediate parts and whole could be said to exist at micro, meso and macro levels. However many systems have many intermediate mesolevels between their lowest microlevel and highest macrolevel. This can be overcome by numbering the levels of assembly as Level 1 (micro), Level 2 (first meso), … , Level m (macro). These numbers are relative since new levels may be created and sometimes levels are collapsed. Apart from part-whole aggregation, system representation includes taxonomic aggregation, with collections of elements, possibly at different levels, being defined to be equivalent and aggregated into classes at higher level. The simplest multilevel sequence has a part-whole assembly relation R combining sets of parts to make many copies of a whole, and those wholes being collected together into the set of R-assembled wholes. For example, R can repeatedly assemble sets of parts into cars with the accumulating set of cars awaiting delivery. This example illustrates the problem we face. In practice R will not be a single relation assembling all the parts into a car in one process. There will be intermediate assemblies such as the engine and this will have intermediate subassemblies such as the carburettor. The problem becomes more difficult when taxonomic aggregation is considered, since this is the imposition of equivalences on abstract or concrete entities which may be almost identical, as in the case of objects produced on a production lines, or very different, as in the case of people with the same roles. To illustrate the problem and our approach consider designing a computer system to process in real time a stream of articles from online newspapers. The objective is abstract the narrative of each article, and to synthesise this with evolving narratives abstracted from previous articles. There is of course a huge literature on text analysis. The architecture we are developing addresses a different problem, namely that of a machine finding structures at different levels in an evolving multilevel representation. E.g., Stuttgart is a part-whole element of the structure called Germany while car making is a taxonomic element of industry. An article on the narrative of Brexit could include reference to <car making, Germany> while another could refer to <industry, Stuttgart>. Here the multilevel structure is essential to make the match. In general the multilevel combinations of words are much more complex than this. An important aspect of the representational dynamics is the possibility of two distinct multilevel narratives colliding with parts at all levels disaggregating and recombining to form a new and possibly more potent narrative . Our presentation will give an overview of the multilevel architecture we have developed and present our results when it applied to the dynamics of multilevel narratives.