I imagine our largest organisms on earth might provide a model.
Our largest organisms are plants or fungi species that have the potential to vegetatively reproce via root (or in the case of fungus, hyphae) networks. For example, the largest organism known now is a large patch (around 100 acres I believe) of aspen trees, all of which are individual ramets of the same organism which has reproduced by sprouting off new trees from its root system. Theoretically, there is NO LIMIT to the size such organisms can reach.
So what do you need to get so large? First of all, you need time! The example above is not only the largest organism, it is the oldest (80,000 yrs). Second, you need stability. By that I mean uniform, favorable conditions in which to grow over a long time. This would be why such organisms grow in soil, as this is a stable environment which is buffered from cataclysmic surface events, such as global temperature swings, wildfires, windstorms etc. Third, you need minimal biotic resistance, so a lack of predators/competitors.
So in answer to your question, something like that whose biomass is largely hidden in some sort of stable matrix.