One of the assumptions of the thermo textbook I'm reading is that the probability of any given microstate of a system is equally likely to occur.
Without further qualification it is not possible to check the thruth of the above sentence. I guess, from what you write after and from the comments, that you are referring to the microstates of an isolated system at equilibrium.
In such a case, the macrostate is not something one can play with, unless the equilibrium conditions are changed. For example, for an isolated fluid system, the equilibrium macrostate is characterized by given values of energy, volume and number of molecules ($U,V,N$). Therefore, once the macrostate has been fixed, at equilibrium nothing else may happen to the system. Certainly the multiplicity of the macrostate cannot vary spontaneously.
It is true that the logarithm of the multipliciy of a macrostate $\Omega$ is conected to the entropy of the system through the celebrated Planck-Boltzmann formula $S=k_B \log \Omega$. But in order to see an increase of entropy, one has to do something to the system. For example, if the fluid is in an isolated, rigid and impenetrable container, and at some time the container increases its volume, the multiplicity of the microstates increases and, the entropy will be increased as well. Similarly for increases of energy or number of particles. However, thsi example shows that there is no problem of "exhausting" the number of microstates, because with the increase of the state function the macrostate depends on, thei numer increases. From the formal point of view this is granted by the positivity of temperature, pressure and by the negative sign of the chemical potential.
Of course this is not the only way of increasing the multiplicity of a macrostate. Even removing some internal constraint one can get the same effect (there is plenty of examples of containers divided into two subsystems in statistical mechanics textbooks). The common feature is that after removal of the constraint, more microstates become available for the total system.
So, in almost all the conditions where one would expect an increase of entropy, there is an accompanying increase of the microstate multiplicity compatible with the new macroscopic conditions.