  While an additional scalar multiplet over and above the Standard Model can
lead to a strong electroweak phase transition, depending on its quantum
numbers, it also potentially confronts crucial constraints from theory and
experiments. Should there exist more than one copy of such a multiplet, it is
possible to predict that number from the requirements of a strong electroweak
phase transition and agreement with the latest constraints. We aim to probe
this specific issue in this study in the context of $N$ degenerate scalar
triplets governed by a global O$(N)$ symmetry. We fold in important constraints
from $h \to \gamma\gamma$ signal strength, dark matter direct detection and
Landau pole behaviour. A combined analysis reveals $N \gtrsim 70$ for a strong
phase transition and consistency with the constraints. We also look into
possible gravitational wave signals in the parameter regions of interest.
