Suppose we have a Lagrangian $L=L(a,b,c,d)$ which is a function of the fields $a,\, b,\,c,\,$ and $d$. We denote the variation of $L$ wrt to a given field, say $a$, i.e. $\frac{\delta L}{\delta a}$, by $E_a$.
Then $L$ is gauge invariant when

$\delta L = \delta a E_a + \delta b E_b +\delta c E_c+\delta d E_d = 0$  (+ tot. derivative).

This gives $\delta d = - (\delta a E_a + \delta b E_b+\delta c E_c)/E_d $  (+ tot. derivative).

The total derivative terms above don't affect the gauge transformation. From the above well-defined equation $\delta d$ can be obtained for arbitrary $\delta a,\, \delta b,$ and $\delta c$ with no necessary relation b/w $\delta a,\, \delta b,$ and $\delta c$. Doesn't this imply that there is an infinite number of gauge transformations? If yes, isn't that absurd?