Even though I live in the US, I like to keep tabs on my country’s military.

As of right now, they have interests in both the Sprut SDM1 and the BMD-4.

Also in the news, Indonesia has been testing the new Kaplan MT (Also known as the Black Tiger in Indonesia).

Is there a place for a Medium Tank at this age and would there be any advantages?

I didn't hear anything about it except Indonesia is going to have Medium Black Tigers tanks.
Last time I check, Indonesia only have 2 types of light tank, 1 main battle tank, and this medium one.
Kaplan MT (If I heard it right) said to be mass-produced soon in Indonesia
So I don't think Mr. President Joko Widodo have another types of med-tanks, but hopefully he will get some.

And having a big celebration of Asian games 2018 (From Indonesia)

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With AMX-13s being phased out, I heard the BMD-4 is for the Marines and the Sprut SDM1 is for the Airborne.

I don’t know why we need the BMD-4 considering we already have the BMP-3 and I don’t know about the Sprut SDM1. Yes, they can do a lot of damage with their autoloading 125mm guns, but its armor isn’t meant to withstand rounds from MBTs and we know how great tanks are with autoloaders when their armor gets penetrated by ATGMs.

Turkey is also offering the Altay MBT to Indonesia but I doubt we’d buy it considering we already have plans to buy more Leopard 2 Revolutions. Included in Indonesia’s shopping list is more Pandur IIs, more BMP-3s, possibly more NASAM IIs, and possibly the S-300 and the F-16V.

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Looks like Mr. President Jokowi has a lot of shopping list, apparently.

About that BMD-4, I just check it in Wikipedia today and here's why Indonesia may need the BMD-4.

The BMD-4 (Russian: "Боевая Машина Десанта-4"; Boyevaya Mashina Desanta-4 literally "Combat Vehicle of the Airborne") is an amphibious infantry fighting vehicle (IFV) originating from post-Cold War Russia.^[1][2] Originally designated as the BMD-3M, the chassis of the BMD-4 is the same as that of the BMD-3, because it was developed on the same basis. This armored fighting vehicle is one of the lightest and one of the most heavily armed in its class, possessing a substantial amount of firepower in comparison to its counterparts. The vehicle was designed to transport Russian Airborne Troops (VDV); increasing its mobility, armament, and protection on the battlefield.

Maybe they need it for amphibious assault.

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So it’s basically a lighter, more mobile BMP-3?

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Kind of.