Giant electromagnetic field enhancements in the vicinity and within layered nanoparticles supporting surface plasmon resonances provide an excellent opportunity for ultra-sensitive Raman spectroscopy. Using metal nanoparticles, enhancement levels of very high sensitivity are achievable but quantitative control over them has traditionally been poor. We propose here multilayered nanospheres with alternating metal-dielectric layers as optimal and easily tailored probes for enhanced Raman scattering, terming these constructs nano-LAMPs (nano-Layered Metal Particles). A theoretical framework based on electromagnetic scattering calculations is used to describe the influence of parameters of the probes, viz. size, composition and spacing of metal and properties of dielectric layers. A recursive formulation of analytical Mie solution is used to evaluate scattering, and the theoretical tunability of electric field enhancement within the spheres is demonstrated as a function of design parameters. An optimization procedure is devised to obtain optimal configurations under fabrication constraints. While demonstrating significant surface enhancement effects, the optical tunability of nano-LAMPs is shown to provide an ability to design probes for multiple excitation frequencies.