Can one be a part-time monk?

if by being a monastic we mean observing the Vinaya, then i believe it's possible as long as Vinaya rules presupposing mandatory expulsion (parajika rules) aren't violated

there're 4 parajika rules

1. Not to have sexual intercourse.
2. Not to steal.
3. Not to commit murder.
4. Not to claim attainments of stages of pure mental concentration
 that have not been achieved.

if by being a part-time monk we mean not being fully committed to spiritual practice, while observing Vinaya nonetheless, then i again believe it's possible

to me it appears that a bhikkhu status is defined not necessarily by genuine and honest spiritual practice but by formal and mechanical observance of the Vinaya and even that may not be entirely flawless

You can be a "practice monk"

Take on the practice of, and learn the precepts of a monk, described in the other answers on this page.

Doing so without formally taking the vows is still "good karma" and doing so will allow you to get an idea of what the actual monks life is like. Taking vows is said to be "stronger" karma, if you keep them.

Figure out which vows or practices you absolutely cannot incorporate into your lay life, set aside "Monk days" to do the full commitment, and lay days, where you do not do these set aside commitments.

Being a "practice monk" is kind of like the light beer of spiritual practice, horrible metaphor I know, but here is what I mean :

You get some of the benefit without any of the risk. You won't have the potential to break any vows. Which is considered "strong bad karma." You also get a preview of the life, and can make the decision from a more informed view point if you ever decide to take on the vows.

Also, if you do take on the vows later, the transition will be easier, as you have practiced.

Visakhuposatha Sutta was for Lady Visaka, Buddha referenced upholding the Uposatha (8 precepts) to be following a life style of an Arahat.

quote from the Sutta

For all their lives the arahants are one-mealers, refrain from eating outside the time, desisting at night,so today I am a one-mealer, refraining from eating outside the time, desisting at night. By this practice, following after the arahants, the Uposatha will be entered on by me.'

It has all the elements you asked,

• living like a monk (for lay person), and
• part time.

Some people become temporary monks -- I think that's a common practice in some countries.

How to become a monk? says, about "temporary bhikkhus",

Naturally, temporary bhikkhus are allowed to keep their possessions, but these must be put aside or entrusted to someone else for the duration of their monastic experience.

He takes the robe for a few days, a few weeks or a few months to dedicate one or more periods of his life to train into monastic life. He is still engaged in various activities, which he does not feel ready to renounce. However, he knows enough to distance himself from them in order to dedicate some time to a life of detachment. If he ascertains that this experience is beneficial to him, he could eventually envisage extending it until the end of his life.

There's a status called Anagarika, which isn't a monk and allows the handling of money (I don't know whether that includes earning/possessing money, or whether it is only handling monetary donations e.g. for the benefit of the monastery).

In Theravada Buddhism, an Anagarika (Pali: anāgārika/ā; lit., "homeless one") is a person who has given up most or all of his worldly possessions and responsibilities to commit full-time to Buddhist practice.

There's also an intermediate status, Maechi.

There's also being a novice monk.

Ten Precepts

The Ten Precepts refer to the precepts or training rules for śrāmaṇeras (novice monks) and śrāmaṇerīs (novice nuns). They are the same in most schools of Buddhism.

The tenth precept is, "Refrain from accepting money."