  We study a $p$-spin model with ferromagnetic coupling and quenched
random-crystal fields for $p \ge 3$ for spin-1 systems. We find that the model
has lines of first order transitions at finite temperature $(T)$ for all $p \ge
3$. For bimodal distribution of the random-crystal field these lines meet at a
\emph{triple point} for weak strength of the crystal field $(\Delta)$. Beyond a
critical strength of $\Delta$, they do not meet and one of the lines ends at a
\emph{critical point} $(T_c)$. Interestingly, we find that on increasing $T$
from $T_c$ keeping other parameters fixed, the system undergoes one more
transition which is first order in its character. The system thus exhibits a
Gardner like transition for a range of parameters for all finite $p \ge 3$. For
$p \to \infty$ the model behaves differently and there is only one random first
order transition at $T = 0$.
