I split LA paragraphs by 'aim'.
For instance, evoking fear (generally of a particular thing); inspiring to action; establishing authority as an expert; discrediting alternatives; etc.
I find aims to be better than arguments because rather than being 'content' focused they are 'effect' (on audience) focused. Also, since the aim is not limited to one specific argument you can draw text examples from across the entire piece (plus any images, layout, paratextual components) to connect in the one paragraph.
I also find this structure works well for comparative analyses, as often pieces will each try to achieve similar aims, but go about them in different ways. Thus the comparative analysis.
Regarding Context, I find one of the easiest ways to turn an expository into something a little more 'pizzazzy' is to contextualise it. For example, an expository only needs a little tweaking in order to become a pretend speech, a debate presentation, an advice/opinion column. Same essential intro and paragraph structure, but you put a specific 'voice' through it and tweak the intros/outros for each point.