Some individuals with pollen allergy experience mouth itching and swelling after eating certain raw fruits, vegetables and tree nuts. The condition is called oral allergy syndrome or pollen-food syndrome.
A certain food allergy as such may increase intestinal permeability (leaky gut syndrome) and allow additional allergens to enter the blood, which can result in multiple food allergies (PubMed, 2006 ; PubMed, 2016).
Infection or stress may increase intestinal permeability and thus induce food allergies in susceptible individuals (PubMed, 2005).
As a side note, food protein-induced enterocolitis syndrome (FPIES) can develop in infants after introducing solid foods and can present with multiple food allergies, which, unlike traditional IgE-mediated allergies, do not cause itching, hives, swelling, coughing or wheezing, but "only" gastrointestinal symptoms, such as diarrhea.