This study introduces the Izaguirre Cytoplasmic Adaptation Hypothesis (ICAH), a novel dual-mechanism theory proposing how cancer cells develop resistance though cytoplasmic communication. It outlines two pathways of adaptive resistance: receptor transfer/signaling and drug dilution via intercellular bridges. The paper includes a detailed experimental step using re/green fluorescence tagging, and mathematical modeling of drug decay across cytoplasmic chains. The ICAH framework suggests novel therapeutic strategies, including a time-based dual injection method to block resistance pathways. This work aims to contribute to the understanding of immune evasion and relapse in cancer treatment.