The GTAP standard model has proved a useful analysis tool and data source for over 20 years. The GTAP model has been updated overtime, but it maintains the structure of a single regional household, with income distributed into three components: government, private and savings-investment expenditures. There has been a need for a more detailed accounting system, especially as it relates to estimating the potential impacts of policies and global shocks on poverty, sustainable and inclusive growth. This paper presents an extension to the GTAP model and its accounting framework to implement distinct and multiple households, split factors of production, foreign aid and remittances, government and household transfer. The model and associated accounting links a household's expenditure to factor incomes (through ownership shares) and taxes. Government expenditure is linked to taxes and foreign aid. The MyGTAP model provides the user more flexibility in: the treatment of government and household savings and spending; the selection of a linear expenditure systems (LES) or a constant difference of elasticities (CDE) demand function\s. The model is incorporated into a RunGTAP application which supports many of RunGTAP's popular programs such as alter-tax, GTAPview and others. The introduction of a split regional household (which does not require splitting data for every region) supports economic analysis based on detailed households, government, factor income, remittances, foreign aid and income transfers. The code can be modified to include multiple regions with unique household structures. This paper documents the model and accounting framework for the use of data output from the MyGTAP data splitting program. It is intended to be used in tandem with a complimentary paper and programs found in:"MyGTAP Data Program: A Program for Customizing and Extending the GTAP Database", GTAP Working Paper No. 79, by Minor, Peter and Terrie Wamsley 2013.