Does Islam define a particular political system or can we just implement any system we want?

Every act is subject to shari'a rules. So to define whether a ruler can delegate his powers, or what are his conditions or what are the types of delegation that can occur and what are those conditions are all subject to the shari'a rules.

So Islam determines that the authority is centralised. Ie one overall ruler. In the Qur'an it mentions this implicitly, "And hold fast by the rope of Allah all together and be not disunited" (3:103) and the sunnah makes this explicit. Abu said al khudry narrated the prophet (saw), "if bayah is given to two khalifahs kill the latter of them" Muslim.

Similarly from the sunnah we see that the prophet (saw) appointed judges, gave them specific authority to judge in some cases but not all. He appointed governors and allowed the taxation to be collected separately from the governor and placed a separate command for the army who then reported back to the prophet (saw). In the wilayahs he appointed provincial rulers (imala). He appointed executive assistance and also delegated assistance who had similar powers to him in enaction of laws but would have to be done under his (saw) general supervision. He appointed people to record inventory, collect and distribute zakat and held council with the representatives of the people and sometimes sought general referendum like in the case of battle of uhud and battle of khandaq.

From this we can see 8 clear categories of the system
1. Khalifah
2. Delegated assistant
3. Executive assistant
4. Governors
5. Army
6. Judges
7. Administrative system
8. Majlis Ul ummah.

We also know that details were derived to explain the conditions of the ppl who could stand for those positions.

So the khalifah had a series of conditions.
1. Male
2. Muslim
3. Sane
4. Mature
5. Capable
6. Just
7. Free

And others also determined they must be from Quraish.