I like Uwe's method, it seems like a comprehensive way to address this situation.
I'd like to suggest an alternative, derivatization. Having done a lot of work with amino acids (zwitterions) there are a variety of methods to choose from. You can use something like FMOC-Cl, which will react with amine groups, and label it with a big, hydrophobic, fluorene group. The amine group becomes a carbamate (neutral) and the compound is now more hydrophobic and only anionic. You can now use anion exchange and/or C18 SPE with a much simpler protocol. Also, if available, desired, you can use fluorescence detection (Ex=260nm, Em=310nm)
To be fair, there are drawbacks to derivatization. First, you must look at reaction efficiency. You must perform the reaction at a pH where the amine is deprotonated, and if the pKa of the amine is high you could be at pH 10. At this high pH, there is a significant amount of OH- around, and this will compete to react with FMOC-Cl (usually this is not a problem for amino acids, can use pH 7.8 ). Also, if you are extracting from plasma, there will certainly be other things in solution that will be derivatized. Second thing to consider is time. The reaction itself seems to take up to an hour, which may or may not be acceptable. It's fine for me, add reagent to solution, go to lunch, come back, and extract.... Third is the potential for MS detection. Usually a derivatized amine will ionize worse than a free amine in ESI (on the other hand, the fluorescence detection is very sensitive, and selective for fluorescent molecules). One last thing, there will always be an extra peak from the product of the reaction of FMOC-Cl and water (FMOC-OH). If the derivatized compound is hydrophobic, it will likely be well separated from this.
A generic procedure. Prepare a reagent solution of FMOC-Cl in an aprotic solvent (acetonitrile, acetone). Prepare an aqueous buffer solution (borate, phosphate, no amine based buffers!) at a pH where the amine of your analyte is deprotonated. Take 500 uL of buffer, 500 uL of acetonitrile, and x uL of plasma (or whatever solution you will derivitize) (I add acetonitrile to the mix because FMOC-Cl is not very soluble in water and when you add the reagent to a solution that is 99% water, it will precipitate and react mainly with water). Mix this solution, and add x uL of the FMOC-Cl solution in acetonitrile (the reaction is 1:1 FMOC to amine group, work out the ratio so there is an excess of reagent).
Other reagents are DANSYL-Cl, and AQC (which it good because it reacts with amines much more quickly than water, SN2 vs. SN1 reaction or something like that)