  An approximate but straight forward projection method to molecular many
alpha-particle states is proposed and the overlap to the shell model space is
determined. The resulting space is in accordance with the shell model, but
still contains states which are not completely symmetric under permutations of
the alpha-particles, which is one reason to call the construction
semi-microscopic. A new contribution is the construction of the 6- and
7-$\alpha$-particle spaces. The errors of the method propagate toward larger
number of alpha-particles and larger shell excitations. In order to show the
effectiveness of the construction proposed, the so obtained spaces are applied,
within an algebraic cluster model, to $^{20}$Ne, $^{24}$Mg and $^{28}$Si, each
treated as a many-alpha-particle system. Former results on $^{12}$C and
$^{16}$O are resumed.
