Jefferson Davis was famously reluctant for Confederate forces to invade the North at all, and my understanding of Lee's motivation for invading Maryland and Pennsylvania was purely to get a better bargaining position and pressure the Union into recognizing the Confederacy.
So - was this pretty much true across the board? Was there a movement, faction, or any individuals who backed secession but actually wanted more (such as a complete take over the Union and essentially go from the United States back to confederacy model rather than having two separate countries). Maybe some believed the Union would never stop until they'd won or were destroyed? It seemed clear early on that the South simply didn't have the capabilities or infrastructure in place to win a protracted conflict since most the manufacturing and industrialization was to the North, perhaps this would have contributed to such a sentiment?
e: Clarified text
While I'm not sure if there were Southern plans to conquer Northern territory, there certainly were Confederates who sought to expand slavery southward into Latin America. An organization named the 'Knights of the Golden Circle' (KGC) were the primary drivers of this policy. Colin Woodward writes about the secret society in his American Nations: A History of the Eleven Rival Regional Cultures of North America.
Founded in 1854 by George W.L. Bickley, a Virginia planter who moved to Cincinnati, the KCG wanted to expand American territory to include all of Mexico, Central America, the Caribbean and the northern parts Colombia and Venezuela, for the purpose of adding more slave states. Mexico alone was planned to have as many as 25 new states added to the U.S, which would have left Congress to be dominated by slave states. This region was also known as the 'Golden Circle', hence their name.
As abolitionist sentiments grew in the years leading up to the Civil War, the KCG began to realize their planned war would never have the full support of the American people so their scheme quickly shifted into secession, then independence, and finally an expansion southward.
Robert Barnwell Rhett, called by Laura White (his biographer), 'the father of secession', was clear about the South's expansionary goals. Days after Lincoln's election, Rhett stated that, "We will expand, as our growth and civilization shall demand – over Mexico – over the isles of the sea – over the far-off Southern tropics – until we shall establish a great Confederation of Republics – the greatest, freest and most useful the world has ever seen."
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Complete takeover? No.
Snatching the odd border state? Yes. Some states, such as Maryland, had slavery but decided to stay in the Union. West Virginia was chopped out of Virgina proper because it was pro-Union. Kentucky was basically split. The Confederacy, of course, considered it to be part of their domain and even represented Kentucky in its Congress. When Bragg launched his Kentucky Campaign he thought it would "liberate" Kentucky and make it a proper state of the CSA (in which he was mistaken).
If the South had crushed the Union at Gettysburg and occupied Washington DC, the question of Maryland, West Virginia and Kentucky would certainly have been on the table.
But that didn't happen. What happened was, that the '63 congress elections in the South saw the rise of a peace party instead, whose adherents wanted to make terms with the North and rejoin the Union, which they thought would be more favorable than if the North conquered and occupied the South.
Maybe some believed the Union would never stop until they'd won or were destroyed?
The popular image is that the South thought Union soldiers to be cowards and no match for proper gentlemen. Considering the initial military blunders of the Union, this is hardly suprising. The aim of the Confedaracy was to make the Union bleed until they stopped (they considered them cowards after all), or (more likely) the UK or France recognized the CSA as an independent nation and would thus force Lincoln to let them go.
Well, since many of the events which are considered to have precipitated the Civil War had to do with whether or not new states would allow slavery, the Confederate goals actually had as much or more to do with the westward expansion of slavery and Southern influence as with preserving slavery and political control in the contemporary Confederacy.