今天吃早饭时候他喝了三杯多豆浆。（我估计他今天得上30次厕所）

You should say "三杯多" in Chinese. "多" is like a suffix used with "数词" and "量词" (classifier / measure word). This expresses a number or quantity that is more than the numeral with a remainder "零头" and usually not exact. When used with “数词" 1~9, it's put after the "量词"; when used with "数词" 10, 20,30..., it's put before the "量词": e.g. 一杯多 三杯多 十多杯 四十多杯 一百多杯 Usually, "多" is used with such numerals. But when you really want to express things like "He's been away for more than 12 years", you should say "他已经离开十二年多了". Thant's because you are talking about more than 12 years but less than 13 years, i.e. the remainder is added to the numeral 2. Then this returns to the rule above about numerals 1~9. So we can say that the position of "多" usually depends on the numeral that the remainder is added to. 多——（用在数量词后）表示有零头：五十～岁，两丈～高，三年～。

今天早饭他喝了三杯多豆浆。