The refs have 大様 and 鷹揚 but not this combination of the characters. Not worth keeping.

ALL ngrams beginning with this term:
大揚	394	  
大揚社	267
大揚げ	195	  
大揚羽	84	  
大揚沼	62	  
大揚力	57	  
大揚沼モリアオガエル	28	  
大揚羽教師	28

Not saying this string of kanji doesn't exist anywhere in Japanese, but I can't find a ref for it besides 難読・異読地名辞典.

大揚 certainly appears in place names. kotobank gives, for example, 大楊村(おおようむら).

Originally came here because of "catholicity". If this is truly [adj-na], then shouldn't the glosses read:
largehearted; liberal; catholic; generous; magnanimous

I would minimally remove "liberal" and "catholic" from the list.

And of course mark [rare], or something.

"大揚な" not in google news, not on twitter, perhaps 10 book results (which include "大揚な母", so maybe?).  But hard to pin down a meaning from so little.

Comments on the inclusion of "catholicity" or "catholic" here are (will be shortly) at 普遍性.

Will recommend deletion in a followup post, but wanted to give edits as well if it stays.

@@ -8 +8 @@
-<reb>おおよう</reb>
+<reb>大揚(おおよう)</reb>
@@ -12,6 +12,4 @@
-<gloss>largeheartedness</gloss>
-<gloss>liberality</gloss>
-<gloss>catholicity</gloss>
-<gloss>generousness</gloss>
-<gloss>generosity</gloss>
-<gloss>magnanimity</gloss>
+<misc>&rare;</misc>
+<gloss>largehearted</gloss>
+<gloss>generous</gloss>
+<gloss>magnanimous</gloss>