Your isomorphism implies that you are factoring the prime $p$ into several primes $p_1,...p_d$, but of course, what you actually factor is the cyclotomic polynomial modulo $p$, i.e., $x^d + 1 = f_1(x) \cdot ... \cdot f_u(x) \pmod p$. Because of the properties of the cyclotomic polynomial, every $f_i$ has the same degree $o$, which is actually equal to the order of $p$ in $\mathbb{Z}_{2d}^*$. And then, the number of slots is $u = o\cdot d$.

So, you cannot encrypt two polynomials of degree $d$ into a single ciphertext. What you can do is to choose $u$ polynomials $m_1,...,m_u$ of degree up to $o-1$, then "pack" them with CRT, obtaining $m \in R_p$, and finally encrypt $m$.

This answer may be helpful.

Your isomorphism implies that you are factoring the prime $p$ into several primes $p_1,...p_d$, but of course, what you actually factor is the cyclotomic polynomial modulo $p$, i.e., $x^d + 1 = f_1(x) \cdot ... \cdot f_u(x) \pmod p$. Because of the properties of the cyclotomic polynomial, every $f_i$ has the same degree $o$, which is actually equal to the order of $p$ in $\mathbb{Z}_{2d}^*$. And then, the number of slots is $u = d / o$.

So, you cannot encrypt two polynomials of degree $d$ into a single ciphertext. What you can do is to choose $u$ polynomials $m_1,...,m_u$ of degree up to $o-1$, then "pack" them with CRT, obtaining $m \in R_p$, and finally encrypt $m$.

This answer may be helpful.