The phrase "grinds in to" is often used to describe a situation where one thing is slowly, gradually being incorporated or melded with another. Some common synonyms for this phrase include "merges with," "assimilates into," "integrates with," "blends with," and "absorbs into." Each of these phrases conveys a slightly different nuance of the underlying meaning, but all refer to the same general concept of two things coming together in a gradual, deliberate way. Whether you're describing the merging of two companies into one or the way a sauce gradually permeates a dish, these synonyms can add variety and specificity to your language.