If I already have a Roth IRA, can I have a traditional IRA too? Can I have more than one of each type?

Yes, you can. However, the limits on annual contributions apply to any combination of traditional and Roth IRA contributions that you make for the year.  For instance, in 2016, the contribution limit is $5,500 (additional $1000 is allowed for IRA-Owners Age 50 and Older).  If you have both Roth and Traditional IRA accounts - the aggregate annual contributions allowed must not exceed $5,500 or $6,500 (IRA-Owners Age 50 and Older).