I am considering using Kuala Lumpur as a "home base" using the "3-month visa free" for EU citizens. I plan to fly into Kuala Lumpur with an exit ticket to my native country in Europe. I do not want to conduct visa runs. 

Would I be able to leave Malaysia to various countries such as Singapore, Taiwan, Korea, Hong Kong and Australia and possibly after each country return to Malaysia all within the 3-month window with no problems at immigration each time? I'd rather not be accused of constant visa runs if I have paid for accommodation for three months in Malaysia. 

A scenario to illustrate what I am attempting to ask:

>I fly into Kuala Lumpur from a third country (arriving on the 25th April), but I have a return ticket from Malaysia to my home country after 3 months (dated 23rd July). *I arrange accommodation for three months in Malaysia.*
>I then travel to Singapore, and then back to Kuala Lumpur, then I fly to Seoul and return to Kuala Lumpur after which I fly to Australia and then back to Malaysia. A month later I fly to Seoul and then return to Malaysia again and so on. 
> After 3 months I return to my own country via Kuala Lumpur. 

However, I imagine immigration might reissue me with visa-free stickers for each time and subsequently accuse me of a visa run but that is not my intention. I intend to holiday in Asia but have KL as a base to return to and recuperate.