If we calculate the Riemann Zeta function along a vertical line in the critical strip, for Re(z)!=0.5, do we ever hit the same point 3 times or more

Question

The line $\zeta(0.5+x \mathrm{i})$ (for $x$ real $>0$) hits the point $0+0i$ an infinite number of times. Along a different line, I'm interested not in hitting zero, but hitting any point more than twice.

If we take $y \in (0,1), y \neq 0.5$, and look at the line $\zeta(y+x i)$ along $x \in \mathbb{R}^+$. Does this line ever hit the same point more than twice?

When playing around with the function, it seemed that this does not happen. But, of course, I didn't try all possibilities.