tasu
1.

To combine or include something additional to what already exists in order to increase quantity or fulfill a requirement, often used in the context of calculations or measurements.

2.

To complete necessary tasks or actions, ensuring that obligations or requirements are adequately addressed.

Example:

60にするためには17に何を足せばよいの。

tsuketasu
1.

To make an addition to something that is already present, enhancing or expanding its existing content or quantity.

2.

To supplement an existing item or situation with further details or elements to provide more completeness or clarity.

3.

To append or attach additional information or components to what is already established, thereby increasing its overall substance.

Example:

「すぐ帰ってくるから」と彼は付け足した。

tsugitasu
1.

To add to something that is already present, effectively increasing its amount or extent, such as supplementing a resource or enhancing a structure.

2.

To make an addition to something that is lacking, often done by inserting or incorporating new elements to improve or complete it.

3.

To augment what already exists by appending or integrating further components, such as expanding written content or lengthening an object.

4.

To fill in gaps or deficiencies by introducing additional material or items in order to achieve a desired fullness or completeness.

つぎtsugitasu
1.

To add more of something to a container or serving in order to fill it up again after it has been partially consumed.

2.

To provide an additional amount of a substance, such as a beverage or food, to ensure there is enough for continued use or consumption.

3.

To refill or restock a resource that has decreased, making it available for ongoing needs or enjoyment.

Example:

「あっ。あたし生卵!」「一個でいいですか?」「うん。足りなくなったらまた注ぎ足すから」