The subject is latus. Definition 6 in OLD is most relevant here:
6 (of solid objects, usu. w. abl.) To be bathed or soaked (in a fluid specified or implied), run, stream, overflow, etc.)
For comparison, there's Ovid Metamorphoses 9.57-58:
vix tamen inserui sudore fluentia multo
bracchia, vix solvi duros a corpore nexus.
...arms streaming (with) ...
Here is an example using all seven cases in a typical way:
Marce, vir feminae panem e furno pistoris Romae dat.
Marcus (voc.), the man (nom.) gives a bread (acc.) from the baker's (gen.) oven (abl.) to the woman (dat.) in Rome (loc.).
Reason for each case:
Marce, vocative: Marcus is being addressed ("Hey Marcus!"), and the vocative is used for ...
Here is another set of examples aimed at the precious bonus points.
Now the cases are in the order they are taught here (nom, acc, gen, dat, abl) so as to help memorization; feel free to permute to your local standards.
The first example uses only first declension feminines.
You can also switch to plural for those endings.
Puella uvam amicae vicinae e ...
The most common usage of impleo is with the accusative and ablative.
The accusative tells you what is being filled.
The ablative tells you with what it is being filled.
N.B. By analogy with plenus + gen. (= "full of X"), sometimes the genitive is used here instead.
Impleo poculum (acc.) vino (abl.) = "I fill the cup with wine."
In my view, there is a subtle difference in meaning. Crucially, note that the adjective propinquus, which expresses a state, selects a dative (e.g., in propinquis urbi montibus (Nep. Han. 5.1)). So the dative nominal associated to the verb appropinquare, which is derived from the adjective propinquus, is used to express the final static position attained by ...
Here is an all-masculine attempt, one word per case, plus a verb:
Vesperi, Attice, imperator populi iussu regi equum pollicebitur.
In the evening, Atticus, the commander, on the people's order, will promise the king a horse.
Vesperi: Locative of vesper.
Attice: Vocative of Atticus, the person to whom the narration is addressed.
As Cerberus points out, plus is an adjective and has therefore the gender and number and case of the main word.
There is also the corresponding adverb plus, which could be seen as the neuter accusative of the adjective.
The word magis is also an adverb, but not synonymous with plus.
I assume your question concerns the adverbial usage, but do bear in mind ...
The usage of plus and other forms like plures, plura seems to be a little complicated and depend on the grammatical number.
Plus can be used as a singular noun or an adverb
The form plus looks like a singular neuter adjective in the nominative/accusative case.
However, what I've read is that this word in the singular is only used as an adverb (the nominative/...
The adjective plus means "more". If you want to say more than, you can either use the (often elliptical) conjunction quam, or an ablative of comparison.
[Ego] habeo plura capita quam homines [capita habent].
[Ego] habeo plura capita quam [ego habeo] caudas.
After quam, you would use the same case as the first element of the comparison, so ego ...