at the same time vs withal

at the same time and withal both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at the same time	No	No	No	Yes
withal	No	No	No	Yes

As adverbs, at the same time and withal are synonyms defined as:

at the same time and withal: despite anything to the contrary (usually preceding a concession)

Other synonyms of at the same time include all the same, even so, however, nevertheless, nonetheless, notwithstanding, still, yet.

at the same time (adverb)	withal (adverb)
at the same instant	together with this
overlapping in duration	despite anything to the contrary (usually preceding a concession)
despite anything to the contrary (usually preceding a concession)