Processed cheeses (PC) are products resulting from the mixing and melting of rennet cheese, emulsifying salts, water, and possibly various additional ingredients. They are considered good vehicles for new ingredients, including plant-based ones. In addition to the health-promoting effects of plant-based ingredients, some of them can also affect positively the quality characteristics of PC (e.g., texture, taste, and consistency) and their addition may reduce the amount of emulsifying salts used. The aim of the study was to determine the possibility of the addition of 0.5, 1.0, 2.0, and 3.0% white mulberry (M), chia (Ch), green barley (GB), or spirulina (S) to PC and the effects on selected characteristics of these products (chemical composition, pH, water activity, color parameters, texture, and sensory properties). In all PC variants, a significance decrease in the dry matter content was observed with an increase in the additive level. The use of plant-based additives allowed us to reduce the addition of emulsifying salts by 50% compared to their typical amounts and the share of rennet cheese in the PC recipe by approximately 18%, which had a beneficial effect on the nutritional value of these products. The use of 3% GB, Ch, or M as additives to PC enabled a reduction in its sodium content by 27, 27, and 42%, respectively, compared to the control cheese. Among the tested additives, GB caused the greatest increase in the hardness of PC (even at the amount of 0.5%), indicating that is beneficial and can be used in the production of sliced PC. All the additives either significantly reduced the adhesiveness of PC or had no effect on this parameter. In terms of sensory characteristics, the highest acceptable addition of GB was 0.5%, and that for S and Ch was 1%, while the addition of M, even at 3%, was assessed very positively. The results of this research may be helpful in the development of new recipes for processed cheeses obtained in industrial conditions.