Yes, you can transfer your current tax base using Props 60, 90 & 110. There are special circumstances that not only allow some to transfer tax base TWICE, the replacement property may be 110% of the sale price (see page 2 of the linked document). Whatever you do, consult a tax/financial planner before taking any action!
Prop 60 provides for the transfer of a base year value from a principal residence to a replacement dwelling within the same county by a homeowner age 55 and over.
Prop 90 authorizes county boards of supervisors to adopt ordinances allowing base year value transfers between different counties, which at the present moment only the following Counties are participating (confirm current status before taking any action): Alameda, Orange, San Mateo, Ventura, Los Angeles, San Diego, Santa Clara.
Generally, a person can use Prop 60 or 90 only once. The sole exception is where a person first received relief for age and then subsequently became severely and permanently disabled and had to move because of the disability.
Prop 110's Section 74.3(b) extends Prop 60 & 90 to "... any person who has a physical disability or impairment, whether from birth or by reason of accident or disease, that results in a functional limitation as to employment or substantially limits one or more major life activities of that person, and that has been diagnosed as permanently affecting the person's ability to function, including, but not limited to, any disability or impairment that affects sight, speech, hearing, or the use of any limbs."
You can read more details here: http://docs.Steven-Anthony.com/Prop60-90-110.pdf