Netherlands Interdisciplinary Demographic Institute's
"Changes in household structure may have profound consequences for a wide range of areas in demography and social policy. Household projection models developed in demography over the past few decades are primarily of the headship rate type, in which the dynamic processes of household formation and dissolution which underlie changes in household structure, essentially are treated as a black box. Back in 1988, NIDI started a pioneering study in order to develop a dynamic household projection model which explicitly focusses on the flows underlying household changes. The model, called LIPRO ('LIfestyle PROjections'), is based on the methodology of multistate demography, but includes several extensions to solve the particular problems of household modelling.
Although originally developed for household projections, the LIPRO computer program can in fact be used for a wide range of calculations in multistate demography. And indeed, LIPRO has been extensively used for various applications, in the Netherlands as well as in many other countries." I have not
used the above-linked LIPRO software myself, but am confident that it is very valuable due to the many projects that it has been used for
(listed on the LIPRO site). I don't know of any other publicly shared/free software that offers direct steps for multistate population projection.
Applied Demography Toolbox