Examples of Epenthesis in Chinese
I cannot think of any epenthesis (增音) examples in Mandarin, but it exists in some dialects of Chinese. Here are some examples in Beijing dialect, from this webpage: 教育部语言文字应用研究所 - 普通话语音和北京语音的界限.

1) 增加声母：


  这儿 “儿” er-her
  女儿 nǚ'er-nǚher （或变为nǚhuor）


2) 增加韵尾：


  把水倒净 “把” bǎ-bǎi
  闭上嘴 “闭” bì-bìn
  枳棘 “棘” ji-jin
  八下里（各方面） “下”xià-xiàn
  告诉 “诉” su-song


3) 增加介音：


  一般儿大（同样大） “般” bān-biān
  动撼（动） “撼” han-huan（或更变hun）
  凑合 “合” he-huo


I think the third case is close to what you are looking for (though it's a dialect but not Mandarin), where additional segments are inserted between initials and finals.

Relevant experiences

I've met many people who will possibly do a similar thing due to they find it hard to pronounce some particular words in a standard way. However, even they know they are inserting syllables, some of them still think that they are speaking Mandarin rather than a dialect. But who can tell? I have no idea how to clearly draw the line.