Yes. Italian adverbs are quite flexible. All of these are correct, though emphasis shifts slightly:
• Capisco profondamente il problema. (standard)
• Profondamente capisco il problema. (stronger “deeply” focus)
• Capisco il problema profondamente. (akin to “I understand the problem, and I do so deeply”)
• Profondamente stresses depth or intensity of understanding, often emotional or philosophical.
• A fondo literally means “to the bottom,” so it conveys a thorough, exhaustive grasp.
• Completamente simply means “completely,” focusing on total coverage rather than depth.
Example: Capisco a fondo il problema = I understand it thoroughly; Capisco completamente il problema = I understand it entirely; Capisco profondamente il problema = I feel its depth/intensity.