Strictly speaking you can’t "get SSIP". Most assessment providers, such as Altius, are members of SSIP and are accredited by SSIP to provide assessment services to vendors. If you have an accreditation from Altius you should be able to obtain registration with other SSIP members for a reduced price and without submitting any further information (well none that relates to CDM requirements anyway, these are already covered by Altius).
Two of our current vendor assessment services currently come under our SSIP accreditation, they are Altius Assure and CDMComply. Once your assessment has been completed and you’ve met the relevant criteria you will automatically, and instantly, be entered into the SSIP database by Altius.