To address the other part of your question...
Whether or not the hosting company lets you change the variable, let's discuss why more than 151 is needed.
If this is a web site then each page should connect, do some stuff, and quickly disconnect. It is a rare web site that need more than 20 connections.
If the web server, such as Apache, is configured poorly, such as
MaxClients = some big number, that that should be fixed. 152 (or even 30) web clients vying for resources will simply bog down, stretching out latency, without imporoving throughput.
If you have "slow" queries that keep connections open a long time; let's look at them; speeding them up may solve your "need" for more than 151 connections.
If you have a seriously overloaded system, consider Replication, wherein you could have multiple Slaves, each providing 151 connections for readonly queries.
PS: MySQL 8.0 will let you set globals in a different way.