It's possible but why not do it in the mainland instead?

go to the psb where you live and get a one month extension. they will usually do it twice.

If you are from one of the Big Five scheduled countries, then there should be no problem getting another tourist visa at the China Visa Office in Hong Kong, particularly since you haven't overstayed your previous visa (good of you to not have done it for sure).

Like some have said, you could apply to the local PSB for another one-month extension as technically under the law you are allowed two one-month extensions before you have to exit.

I am not sure that I see a problem here either way.  Please let us know how things turned out.

you are on the right rack.. you do not need help..just go with your plan

I did get L visa from HK Embassy in March this year. However, HK Embassy was very stingy, and grant only 14 days L visa. HK Embassy received Tianjin Middle School letter about their intentions to employ me, and request for 30 days visa, necessary for gathering all documents for Z visa.

I don't hold passport from big 5, and I am assuming that was the reason for 14 days L.

Doesn't matter what, you should be ready to apply for Z in HK. As I know, Medical exam less than 6 months old should be satisfactory to HK Embassy's requirements. I suggest, you try and get Embassy's Medical form, and complete Medical exam in China. 

I completed Medical exam in September in HK for cost of approx. 2200 Rmb. Same exam cost me only 400 Rmb in Anshan, Liaoning last year.

Employee at HK Embassy asked me for Medical exam not older than 6 months.

You must have Embassy's form of Medical exam signed by MD and stamped by Hospital. 

Thank you all for you advice and input :D  Everything worked out fine and the HK visa office gave me a 1 month L visa.  My boyfriend is Chinese and I just had him write an "invitation letter" asking for me to stay with him and explaining that I am waiting for the documents from my new job.

So now I am still waiting for my job to prepare everything and in about two weeks I will go again to get my Z visa.

szj_girl, thanks for the follow-up for sure.  Glad it went smoothly.  Best of luck.

Good time to go traveling mate! There are always delays and complications. I almost think it would be easier and better just to get a long term business visa and work from that. The ever so elusive Z visa almost seems like too much hassle. And the breaks? Annoyance!

To "Fordicus" above, the Z visa is hardly elusive.  It is readily acquired by an employer on behalf of an employee where the employee meets the criteria for a Z visa and where the employer possesses the required documents to obtain a Z visa.

F visas are usually acquired by those who need to fly under the radar, whether they be from countries that are not usually considered eligible for Z visas,  at least in terms of ESL, or where the employer does not have an Alien Work Authorization, or simply where the prospective employee does not meet the minimum standards for employment.