While you have been given some proper advice, it does not solve your problem of lack of volume.
Yamaha rxv685 specs are here.
Yamaha NS-IC800 speakers here.
That is a very large room with high ceilings. The Yamaha speakers are just average and ok for background music but at high volumes you could damage those speakers depending on how they are wired. They are rated 50W nominal while the receiver can output 90W per channel.
What we need to know is how the speakers are currently wired. If the pairs are wired in series (in a daisy-chain style, receiver plus to speaker A +, speaker A - to speaker B +, speaker B - to receiver -) then you are splitting the power over two speakers, so basically half of 90W maximum to each speaker, or 45W maximum per speaker. That will protect the speakers from being damaged but then you are under utilizing your receiver. If the speakers are wired in parallel (receiver + to speaker A + and speaker B +, speaker A - and speaker B - to receiver -) then the speaker impedance drops from 8 ohms to 4 ohms and you may over drive the amplifier.
If you have 4 separate pairs of wires running from the speakers to the receiver, then there is a way to use 4 channels of amplification instead of just two. You connect one pair of speakers to the front left and right speakers connections on the receiver and connect the other pair of speakers to the surround left and right. You then set the audio mode of the receiver to all-channel-stereo. This sends the same level of signal to both the front and surround speakers so that you get the same volume from all four and use 4 channels of amplification. If the receiver is changed to any other surround mode, you will loose volume from the surround pair.
You could also connect one pair of speakers to Zone 2 (instead of surround) and then enable "Party Mode" in the receiver. That should also output the same sound level to all four speakers using 4 amplifiers (but there is probably separate volume control for the main zone and zone 2, so that is not ideal as you need to turn up each zone individually).
90W should be enough to fill your 5m x 5m space when sitting underneath but you will not fill that entire 10m x 10m room with 4 small speakers, so you need to set your expectations accordingly. We need to know what country you are in to recommend a speaker upgrade. There are definitely better options out there, although $1000 may not be enough for all 4 unless you can find a good sale.
Your initial question was about adding an amplifier. The Yamaha does have a Pre-Out connection for the front channels, so yes, it supports adding a 2-channel amplifier with more power. I would not recommend that in this case. You need to double your power to achieve a 3dB gain in volume, so you would needing to add an amp with 200W per channel or more to make a significant difference, and then you get into the issue of whether those Yamaha speakers can handle that much power.
