In Rational Homotopy Theory, there is a model of cell-attachment. In the book "Rational Homotopy Theory", the model is given for attaching only one cell, which is:
If $X$ is simply connected space with rational homology of finite type and $Y=X\cup_{\alpha} e^n$, where $\alpha\in\pi_{n-1}(X)$ and if $(\Lambda V,d)$ is the minimal model of $X$, then $(\Lambda V\oplus u_{\alpha},d_{\alpha})$ is a commutative model of $Y$. Now, instead of one cell, if we attach finite number of cells of same dimension, then is $(\Lambda V\oplus u_{\alpha_1}\oplus u_{\alpha_2}\oplus \dots\oplus u_{\alpha_r},d_{\alpha})$, $d_{\alpha}(v)=d(v)+\langle\alpha_1;v\rangle u_1+\langle\alpha_2;v\rangle e_2+\dots +\langle\alpha_r;v\rangle u_r$ a commutative model of $Y=X\cup(e_1\cup e_2\cup \dots \cup e_r)$?