I'm a local grad for a small private uni as well and managed to get offer into big4.
A few things you can improve your chances with big4
1) Maintain good CGPA - second upper and above is a must
2) Join any Big 4 or MNC challenge/competition to improve your resume
3) Go for internship - whether small/big firm it doesn't matter, it shows that you are motivated and willing to learn
4) Organise event or hold position in university club/society
5) Start your professional papers early - there are plenty of professional programme that partner with university which encourage final year students to undertake their professional paper (i.e. ACCA Accelerate or other professional body such as CPA, ICAEW, MICPA, CIMA) They all have different partnership with different university. Start early and this will show employer that you are taking initiative to build your career.
6) Improve on your command of language.

There are plenty of ways for local grad to build up your own resume. Is just whether we are willing to take up the initiative to improve ourselves. Overseas grad may have advantage but I have also seen how good their resume can be not only because of the university they are from but also them taking initiative to undertake different internship and leadership position to improve their resume.

This post has been edited by unknown_228: Mar 4 2017, 04:28 PM