Defining a formal model for concurrency in programming languages that addresses conflicting requirements from programmers, compilers, and architectures has been a long-standing research question. It is widely believed that traditional axiomatic per-execution models that reason about individual executions do not suffice to address these conflicting requirements. Consequently, several multi-execution models were proposed that reason about multiple executions together. Although multi-execution models were major breakthroughs in satisfying several desired properties, these models are complicated, challenging to adapt to existing language specifications given in per-execution style, and they are typically not friendly to automated reasoning tools. In response, we propose a re-execution-based memory model (XMM). Debunking the beliefs around per-execution and multi-execution models, XMM is (almost) a per-execution model. XMM reasons about individual executions, but unlike traditional per-execution models, it relates executions by a re-execution principle. As such, the memory consistency axioms and the out-of-order re-execution mechanics are orthogonal in XMM, allowing to use it as a semantic framework parameterized by a given axiomatic memory model. We instantiated the XMM framework for the RC20 language model, and proved that the resulting model XC20 provides DRF guarantees and allows standard hardware mappings and compiler optimizations. Noteworthy, XC20 is the first model of its kind that also supports thread sequentialization optimization. Moreover, XC20 is also amenable to automated reasoning. To demonstrate this, we developed a sound model checker XMC and evaluated it on several concurrency benchmarks.