"Biblically, is there any scriptural evidence against a man having a concubine?" Yes, because sexual relations apart from a spouse are forbidden, and concubinage obviously falls outside of marriage. These verses don't speak of concubinage specifically, but they all speak against sexual relations outside of marriage. As such, concubinage is adultery.
You know the commandments: ‘Do not commit adultery, Do not murder, Do
not steal, Do not bear false witness, Honor your father and mother.
1 Cor. 6:18
Flee fornication. Every sin that a man doeth is without the body; but
he that committeth fornication sinneth against his own body.
1 Cor. 7:1-2
Now concerning the matters about which you wrote: “It is good for a
man not to have sexual relations with a woman.” But because of the
temptation to sexual immorality, each man should have his own wife and
each woman her own husband.
1 Cor. 7:8-9
To the unmarried and the widows I say that it is good for them to
remain single as I am. But if they cannot exercise self-control, they
should marry. For it is better to marry than to burn with passion.
1 Cor. 6:9-10
Or do you not know that the unrighteous will not inherit the kingdom
of God? Do not be deceived: neither the sexually immoral, nor
idolaters, nor adulterers, nor men who practice homosexuality, nor
thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers
will inherit the kingdom of God.