You can drop the modal after its first and retain the sense if you concatenate verbs in the same clause.
On Sunday I will finish my homework and visit Sally.
Both verbs are in the simple future and mean exactly the the same as
On Sunday, I will finish my homework and will visit Sally.
The second "will" may be dropped.
Unfortunately, in the case of your sentence, it is not clear why it should be in the present perfect. Moreover, if you do want the verbs to be in the present perfect, "drank" needs to be "drunk."
I've paid a visit, played chess, drunk an espresso, and bought a couple of souvenirs
means the same thing as
I've paid a visit, have played chess, have drunk an espresso, and have bought a couple of souvenirs
I will admit, however, that only the most careful speakers are likely to catch that "drunk" is technically correct when the modal indicating the present perfect is dropped. One reason for that is that is that the use of the present perfect seems odd in this case.
EDIT: The OP has asked a question about the use of the present perfect based on my questioning why it was used in the original question.
The use of the present perfect in English is complex. With respect to verbs that may have a continuous aspect as a result of their meaning, the present perfect can represent something that started in the past in the past and continues to this day.
I have loved her since the day I met her
means that I still love her.
I loved her
implies that I no longer do.
The present perfect may be used to describe a completed past action that is connected to a present situation
I can't pay you right now because I have lost my wallet.
The present perfect may also be used to emphasize that an action has been completed.
I have done my homework
stresses that it is complete.
The present perfect may also be used to represent actions completed in the recent past. But recent is relative.
I have graduated from college
may mean last week or last month or maybe even last year. It depends on context. In this case, graduation is a major event, a rite of passage, and so recent is defined in the context of the life of an adult. With respect to actions of less import, recent may reduce to minutes or even seconds.
I finally kissed her
may refer to something that happened within the last 15 minutes.
There is no rule that rigidly defines recent in terms of a calendar or a clock.