You can't have the same period. If it's the same period, then whatever the visual angle between them is initially is the angle forever.
You probably can't have a small difference in periods. They tend to be unstable.
A 1:2:4 resonance and a 1:3:5 resonance may work. But having the same phase, means that planet, moon 1, moon 2, moon 3 will have to be close to a straight line. To be also either new or full you have to have the sun in that line too.
Lets assume that being within 10 degrees counts as 'being in phase' (The difference between phases of the moon changes 12 degrees a day)
Let's use the 1:2:4 resonance, and we'll make the periods 1 week, 2 weeks and 4 weeks. So the outer moon has about the same period as Luna. If the resonance was perfect, they would all line up once a month. Whether it was a new or full moon depends on the relation between the orbital period of Outer compared to the year. If the relationship is not a resonance, then on the average 1/36 (360 degrees / 10 degrees) of the lineups will also be either new or full.
However the lineups will not be distributed well. They may be an average of every 3 years, but you might get 3-6 in close succession with half a year between them, then go 10-20 years between them.
There would be a pattern to it. The 10 degree limit means that lineups would take whatever time it takes the fastest moon to move 10 degrees. So 1/36 of a week. A few hours. If the year were 10 months long then the lineup from one month to another would move 36 degrees across the sky.
Remember that only half the lineups will be visible. The other half will be on the back side of the planet from any one point.
It's unlikely that the resonance will be perfect, so you may get long periods where there are no lineups.
As an aside, search this site for "Can a planet have multiple large moons" I asked that question some years ago both here, on physics.SE and a couple of physics forums. The upshot is, "No, it's unstable." and one moon either gets ejected, hits the planet or another moon.