Strictly speaking, a unique nullable column (or set of columns) can be NULL (or a record of NULLs) only once, since having the same value (and this includes NULL) more than once obviously violates the unique constraint.
However, that doesn't mean the concept of "unique nullable columns" is valid; to actually implement it in any relational database we just have to bear in mind that this kind of databases are meant to be normalized to properly work, and normalization usually involves the addition of several (non-entity) extra tables to establish relationships between the entities.
Let's work a basic example considering only one "unique nullable column", it's easy to expand it to more such columns.
Suppose we the information represented by a table like this:
create table the_entity_incorrect
(
id integer,
uniqnull integer null, /* we want this to be "unique and nullable" */
primary key (id)
);
We can do it by putting uniqnull apart and adding a second table to establish a relationship between uniqnull values and the_entity (rather than having uniqnull "inside" the_entity):
create table the_entity
(
id integer,
primary key(id)
);
create table the_relation
(
the_entity_id integer not null,
uniqnull integer not null,
unique(the_entity_id),
unique(uniqnull),
/* primary key can be both or either of the_entity_id or uniqnull */
primary key (the_entity_id, uniqnull),
foreign key (the_entity_id) references the_entity(id)
);
To associate a value of uniqnull to a row in the_entity we need to also add a row in the_relation.
For rows in the_entity were no uniqnull values are associated (i.e. for the ones we would put NULL in the_entity_incorrect) we simply do not add a row in the_relation.
Note that values for uniqnull will be unique for all the_relation, and also notice that for each value in the_entity there can be at most one value in the_relation, since the primary and foreign keys on it enforce this.
Then, if a value of 5 for uniqnull is to be associated with an the_entity id of 3, we need to:
start transaction;
insert into the_entity (id) values (3);
insert into the_relation (the_entity_id, uniqnull) values (3, 5);
commit;
And, if an id value of 10 for the_entity has no uniqnull counterpart, we only do:
start transaction;
insert into the_entity (id) values (10);
commit;
To denormalize this information and obtain the data a table like the_entity_incorrect would hold, we need to:
select
id, uniqnull
from
the_entity left outer join the_relation
on
the_entity.id = the_relation.the_entity_id
;
The "left outer join" operator ensures all rows from the_entity will appear in the result, putting NULL in the uniqnull column when no matching columns are present in the_relation.
Remember, any effort spent for some days (or weeks or months) in designing a well normalized database (and the corresponding denormalizing views and procedures) will save you years (or decades) of pain and wasted resources.