I have a full time construction job and I want to take on an additional part-time job so I don't have to live paycheck to paycheck. If I were to be laid off from my full-time job could I still collect unemployment somehow?

Not normally, but it depends on the number of hours the part time employs.

It will depend on the laws of the state you live (if in the US) in GA for example, you may file, but have to report your earnings from the part time job, If you make over a certain level you will not collect at all, or it is reduced by part of the earnings.