Keynesian Cross and Balanced Budget Multiplier
The fiscal multiplier in (iv) would arise from

$$ Y = C+I+G$$

$$ Y = a + c(Y-T)-d\alpha Y +G+I.$$

This can be rearranged as 

$$Y(1-c+d\alpha)=a-cT+G+I,$$

and, therefore, the fiscal multiplier would be

$$\frac{1}{1-c+d\alpha}.$$

In order for this to equal $1$, you just need $d\alpha=c.$

Note that setting $d\alpha=c$ in your "multiplier" does not yield 1:

$$\frac{1}{1-c}+\frac{1}{1-d\alpha}=\frac{1}{1-c}+\frac{1}{1-c}=\frac{2}{1-c}.$$