It seems like a rather rare prefix, really. I tried to count all the verbs that have it in my Kenkyusha dictionary (I could go for a larger one, but I didn't want rare verbs) and I've got these:
- もてあそぶ (sometimes in Kanji: 弄ぶ) - to toy with something or someone
- 持て余す - to be too much (especially: too much to handle)
- もてなす (持て成す) - to treat, to welcome
- もてはやす (持て囃す) 持て囃す- to extol
Four verbs in a medium-sized dictionary, that's it. This "prefix" definitely isn't very productive, and you definitely can't use it with any verbs. In fact, it's just the first part of a tiny closed list of compound verbs that come as is. This is different from a productive verb prefix that can be used to create compounds ad-hoc such as あえて (e.g. in あえて言う dare to say, go ahead and say).
Another thing that makes もて different from a regular prefix is that it doesn't change the meaning of the following verb in a consistent manner. While あえて always adds the same element of daring, もて isn't simply intensifying all verbs in the same way. You can probably say it's an intensifier in all the verbs in my list except for (持て成す), but the intensification works differently in any place and you can't predict the meaning of the compound verb by just knowing what the verb joined with もて means.