An approximate but straight forward projection method to molecular many α-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 α-particles, which is one reason to call the construction semi-microscopic. A new contribution is the construction of the 6-and 7-α-particle spaces. The errors of the method propagate toward larger number of α-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-α-particle system. Former results on 12 C and 16 O are resumed