Are there species that occupy several roles in the food hierarchy?
By role, I am referring to producer, primary consumer, secondary consumer, tertiary consumer, quaternary consumer and so on.
Examples of more specific questions
Are there species that are both primary and secondary consumer?
Are there species that are primary consumer, secondary consumer and a tertiary consumer?
Are there species that are both producer and primary consumer?
Food hierarchy and food web
Ecological trophic interactions are better represented by food webs rather than simple hierarchical relationships. As a consequence, the concepts of primary/secondary/tertiary/... consumers sometimes poorly apply to reality.
Obligate and Optional
Many species are able to feed on a various source of nutrients. As a consequence, a species can be a primary consumer under one environmental condition and be a secondary consumer under another. Such species might eventually almost never be both a primary and a secondary consumer at the same time and it renders the classification of species into one or another category a little more arbitrary.
How much does one need to eat to belong to a given category?
Note also that species like the cat, for example, are generally considered as being just carnivorous while in reality they often eat a very small amount of plant material. They also indirectly consume plant materials that are present within the gut of their preys. Such cases make the categorization more arbitrary again
Primary, secondary and tertiary consumer
This one is pretty easy. Humans, pigs, bears, corvids and catfish are all examples of species that are primary, secondary and tertiary consumer all in the same time. In other words, humans are omnivorous.
I am currently preparing a stew for tonight $\ddot \smile$. There are a number of vegetables and a little bit of pork (which itself is omnivorous). Tomorrow, I'll make some salmon (which is a secondary consumer as it mainly feeds on zooplankton).
Producer and secondary consumer
Carnivorous plants are able to photosynthesize and to capture animals. Most animals they capture are often best described as a primary consumer but some carnivorous plants small fish that feed on phytoplankton or even mice and frogs according to this video.
Producer and primary consumer
Parasitic plants (such as the common holly) are able to both photosynthesize and parasitize other primary consumers (it therefore also is a primary consumer if we equate parasitism to consumerism).
The eastern emerald elysia (a sea slug) feed on algae and is able to photosynthesize (using the chloroplasts of its preys).
Producer, primary consumer and secondary consumer
I cannot think of any examples right now but I would bet that it exists (eventually in a chemoautotroph species and eventually in a species that has a various life cycle).
First of all, apart from primary producers, it can sometimes be difficult to assign an exact position or role to organisms in a tropic web or net since trophic levels might be diffuse or tangled. Most obviously, omnivorism is defined as organisms that eat from different food types, which in practice often means they eat from several trophic levels. Besides what is mentioned in the other answers, you also need to add species that shift their trophic role over their life history, which is e.g. the case for many species of fish, where juveniles are primary consumers (of e.g. plancton), while adults are secondary or tertiary consumers. The same situation is found in frogs (tadpoles vs adults) and many other organism groups. The basis for these shifts is often a change in body size (so trophic position is partially a function of body size), and these shifts are often discussed under the label ontogenetic niche shifts (see Werner & Gilliam, 1984). Functionally, such trophic shifts also means that the species can exploit widely different food sources over its life course, which will decrease the amount of intraspecific competition.
Another example of life-history shifts in the feeding hierarchy are species that change their trophic level when they change habitat. This is the case for salmon that migrate between marine and freshwater habitats. A third example is species that have intra-species predation (see e.g. Polis, 1981), which is also called cannibalism. This is, for instance, common in perch (Persson et al, 2000).
See this as a complement to Remi.b's answer.
To follow up with Remi.b's answer, there is an example of an organism that is a combination of producer + primary consumer + secondary consumer:
Bladderwort (Utricularia spp.) is a carnivorous plant that photosynthesizes and is known to eat insects, fish and tadpoles. In addition, research by Marianne Peroutka suggests these plants also eat algae. (see here and here) .
Others have also noticed other carnivorous plants ingesting plant parts, possibly suggesting that more than one genera of plant fits this combo of trophic roles.
