Solving the steady-state problem of asset allocation for two kinds of households

When I set up two kinds of households in the model and both bought treasury bonds at the same interest rate, I found that I could not find out the amount of treasury bonds purchased by each household in steady state, but only the total amount of treasury bonds. In this case, how should the model be changed in order to make further analysis?

I am not sure I understand the problem. What determines the supply of bonds? And why do you think that the wealth of agents is endogenously determined in steady state? Usually, there is no mechanism to force agents to a particular steady state value as the permanent income hypothesis makes agents just consume the annuity. You would need to somehow endogenize that choice.