Can I ask for higher salary than I asked in the first interview?
You may get a higher salary only if you can present some logical or practical reasons for that increase. However, if you can't provide the company with a good explanation, then not only you may not get a higher salary, but also the company may withdraw the offer and select other applicants over you for the job.
Yes, I have seen job offers being withdrawn from people who ask for a higher salary (after they set their initial salary requirements in the first interview with HR) and who can't give the company a good reason for the increase. Please note that, very often, there are many well-qualified candidates who compete for 1 particular job. You are not the only star player in the game.
Here are 2 examples with good reasons to ask for an increase in salary:
For example, if you can show the company that Google search and
other websites such as Glassdoor consistently show that the average
salary for workers with the same skillsets and experiences as yours
in the same city is a lot higher than the initial salary you asked
for, then you may have a good reason to do so.
If this is the case, then you could simply tell them that you did
not do a careful research for the salary or you miscalculated the
salary vs. the cost of living for that city when you first provided
them with your initial salary requirement, and now you would like to
ask for an adjustment.
Another good example would be during the interviews, you find out
that the job requires you to travel a lot more than what the
original job description says. This means the company should
compensate you more. So, it is reasonable to ask for a higher
salary.
If you can't come up with a good reason to ask for a higher salary, then the company won't think very high of you.
The reason is similar to this case: Suppose you are the owner of a small company with less than 15 employees. Now, you want to hire another worker. In the first interview, the candidate says his salary requirement is $70,000. After you spend lots of time to interview him, you want to give him an offer for $70,000. Guess what ? Now, the candidate says "Not so fast. I want a salary of $80,000." What would you do ? Will you withdraw the offer to avoid all the unpredictable drama with this candidate ? Would it be faster and safer to hire a different candidate who takes the job offer with the exact salary he sets initially ?
It is important to note that, at this point, you have not got the job offer from that company yet. So, everything is just hypothetical for now.