The phrase "give backing to" can be substituted with various synonyms depending on the context. For example, "supporting," "endorsing," and "encouraging," can all be used interchangeably for the phrase. Alternatively, the phrase may be rephrased with words like "upholding," "championing," and "advocating." Other synonyms that can be used for "give backing to" include "sponsoring," "backing up," and "promoting." These words can be effectively used in different contexts to convey the meaning of the original phrase. When writing, it's always essential to choose the right synonyms carefully in order to make sure that the meaning is preserved.