Many schools, at least in the US, frown upon students earning a second BS/BA. I tried and was basically told by an admissions counselor that I probably wouldn't be accepted. I was welcome to apply for a master's degree and take any undergraduate courses I needed once I had been provisionally accepted into that program, however. But I wouldn't have earned a BS. I suspect that this might have to do with financial aid rules, but I'm really not sure.
I ended up taking some post-bac courses at the university I'd gone to for my BA then going directly into an MS program.
as i said in another reply, this "anti-second BS" thing might have been true years ago but as i've personally discovered, it's not true at all. yes, some schools don't have a clear-cut program for readmission for second degrees, but it seems many schools now do. i'm personally returning for a second degree in CSC, and i didn't even have to go through any kind of admissions procedure - just fill in a one-page form to my alma mater and 3 weeks later they informed me it's approved and so i'm returning for my second BS in fall this year. it's definitely very possible today and if you want more details, please feel free to PM me.
1. Getting re-admitted to ones alma mater is simpler than a new school (given that these are adults going back to school who may well have moved and established families, their alma mater quite possibly is no longer an option)
2. How many credits were waived? This is a pretty serious sticking point, as anything > 2 year full time equivalent becomes a major time commitment & investment. I would also point out here that this can vary significantly by institution, unfortunately.
3. Many undergrad classes don't support a fully flex part time schedule (or, severely limit their evening & part time options). This becomes increasingly important in this scenario.
While there may or may not be an admission-department policy or stigma against second undergrad degrees, the system is by and large certainly not geared to encourage it as of present.
I ended up taking some post-bac courses at the university I'd gone to for my BA then going directly into an MS program.