These extracts from the 2005 AC-21 Memo probably cover the main points:
Answer: No. As noted above the relevant inquiry is if the new position is the same or similar occupational classification to the alien’s I-140 employment. A difference in the wage offered on the approved labor certification, initial I-140 and the new employment cannot be used as a basis of a denial. However, a substantial discrepancy between the previous and the new wage may be taken into consideration as a factor in determining if the new employment is “same or similar.”
Question 7. Should service centers or district offices request proof of “ability to pay” from successor employers in I-140 portability cases, in other words, from the new company/employer to which someone has ported?
Answer: No. The relevant inquiry is whether the new position is in the same or similar occupational classification as the alien’s I-140 employment. It may be appropriate to confirm the legitimacy of a new employer and the job offer through an RFE to the adjustment applicant for relevant information about these issues. In an adjustment setting, public charge is also a relevant inquiry.
Question 8. Can an alien port to self-employment under INA §204(j)?
Answer: Yes, as long as the requirements are met.
First, the key is whether the employment is in a "same or similar" occupational classification as the job for which the original I-140 petition was filed.
Second, it may be appropriate to confirm that the new employer and the job offer are legitimate through an RFE to the adjustment applicant for relevant information about these issues.
Third, as with any portability case, USCIS will focus on whether the I-140 petition represented the truly intended employment at the time of the filing of both the I-140 and the I-485. This means that, as of the time of the filing of the I-140 and at the time of filing the I-485 if not filed concurrently, the I-140 petitioner must have had the intent to employ the beneficiary, and the alien must have intended to undertake the employment, upon adjustment. Adjudicators should not presume absence of such intent and may take the I-140 and supporting documents themselves as prima facie evidence of such intent, but in appropriate cases additional evidence or investigation may be appropriate.
Question 14. Must the alien have a new offer of employment at the time the I-485 is being adjudicated under the I-140 portability provisions?
Answer: Yes. The alien cannot still be looking for “same or similar” employment at the time the I-485 is being adjudicated under the adjustment portability provisions. The alien must be able to show there is a new valid offer of employment at the time the I-485 is adjudicated.