You have a fairly large room with a lot of space to fill.
I think the avr will have a hard time filling all that space.
I'd spend more on the avr and not worry at this time about adding an amplifier. If you're going that route I'd rather have separates if going that route.
You'll find $4k doesn't go far for quality in a larger room.
TV: Sony XBR 65X950G, AVR: Marantz SR5011, Speakers: front/Paradigm Prestige 15B bookshelf, center/Paradigm Prestige 45C, surround/Paradigm Atom, sub/SVS SB3000, DVD: LG UBK 90 UHD DVD Player, Media Player: Zidoo Z9S, Remote: Logitech Harmony Ultimate Home