Commentary for Makhshirin 5:1

מי שטבל בנהר – and the water that is upon him makes him susceptible [for ritual impurity] for they (i.e., the waters) were acceptable/intentional.

One who immersed himself in a river and then there was in front of him another river and he crossed it, the second [water] purifies the first [water].
If his fellow pushed him in during exercise or his beast [pushed him in], the second [water] purifies the first [water].
But if [he did it] out of playfulness, it comes under the law of ‘if water be put’.
Section one: When he gets out of the first river, the water that remains on his body causes produce to be susceptible to impurity, because he intentionally went into the river to bathe. Then he has to cross another river but he doesn't need this river to bathe. The water from the second river does not cause susceptibility because he didn't want to get wet, he just wanted to cross. The water on him from the second river therefore purifies, or causes not to make susceptible, the water from the first river.
Section two: A person comes up out of the water after bathing. Then he gets pushed in again, either because he and his friend were exercising or his animal pushes him in. The second time in the river is not something he wanted, so this water "purifies" the water that was on him from the first time. Note that here he goes into the same river twice the water from the first time does cause susceptibility but the water from the second time does not.
However, if he and his friend were just playing around, then entering the water is something that they wanted. Therefore, this water too causes susceptibility. Again, it is all a matter of intent.

והיה לפניו נהר אחר, ועבר בו – but the waters that are upon him from the second river are into acceptable/intentional and do not make him susceptible [for ritual impurity].

טיהרו – the waters of the second river [purified him], waters that were brought up with him from the [initial] ritual immersion, and neither set of waters make him susceptible [for ritual impurity].

דחיו – he (i.e., the other person, who was inebriated) pushed him [into the water].

לשכרו – that his friend was inebriated and through his drunkenness pushed him and caused him to fall into the river.

וכן לבהמתו – that as a result of his drunkenness, he caused his [fellow’s] animal to fall into the river, and the waters of ritual immersions that were upon him and upon his animal were intentional.

טיהרו שניים – that were [upon him] through the drunkenness [of his fellow] and not acceptable/intentional.

את הראשונים –[the waters of the first river which were made insusceptible] which were not acceptable/intentional

ואם כמשחק – his fellow [in jest] pushed him into the river or his animal/beast, also the second waters are under the law of “when water is put” (Leviticus 11:38), and all of them (both the first and the second set of waters) are acceptable/intentional.