I would start doing comparative benchmarks between Intel i7 and AMD Ryzen for gaming, first. Then I'd look at the prices on available late-model graphics cards (if you can find any). While you're doing all that, keep saving. I have a hard time believing that you're going to get a decent 3- to 5-boxing rig for less than $1500-1700US if you're paying a 40% premium already. The basic system I'd build for multiboxing that I priced for a friend last week was about $1300-1600 on the American market. Granted, it's not an ALC (absolute lowest cost) system but it's got enough overhead and quality that you won't get screwed if the next expansion increases the requirements again.

Based on my recent poking around on Amazon for my preferred components:

CPU = $300-400 for 5-boxing
GPU = OMG don't ask; I'd estimate $650-800 if you can find a GTX1070 8GB card or AMD equivalent at currently insane market prices; $450 if you can find one squirreled away somewhere
RAM = $200-450 (16GB of 2133MHz up through 32GB of 3000MHz)
HDD = $100 for a couple of standard HDDs or one Samsung 250GB SSD
PSU = $120-160 (650W-850W)
Motherboard = $125-300 depending on features
Case = $50-100 depending on features

So, if you went absolute minimum recommended quality levels (no Chinesium bargain-bin junk) and didn't buy a monitor, you might be able to get by on about $1500 BEFORE your country's market premiums if you want any longevity and stability out of it.

My 2 copper, anyway.